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\title{Package \texttt{np} FAQ} \date{\today} \author{Jeffrey S.~Racine}

\begin{document}

\maketitle

\tableofcontents

\onehalfspacing

\section{Overview and Current Version}

This set of frequently asked questions is intended to help users who
are encountering unexpected or undesired behavior when trying to use
the \texttt{np} package.

Many of the underlying C routines have been extensively tested over
the past two decades. However, the \texttt{R} 'hooks' needed to call
these routines along with processing of the data required for a
seamless user experience may produce unexpected or undesired results
in some settings.

If you encounter any issues with the \texttt{np} package, kindly first
ensure that you have the most recent version of \texttt{np},
\texttt{R}, and \texttt{RStudio} (if appropriate) installed. Sometimes
issues encountered using outdated versions of software have been
resolved in the current versions, so this is the first thing one ought
to investigate when the unexpected occurs.

Having ensured that the problem persists with the most recently
available versions of all software involved, kindly report any issues
you encounter to me, and \textsl{please include} your code, data,
version of the \texttt{np} package, version of \texttt{R}, and
operating system (with version number) used so that I can help track
down any such issues
(\href{mailto:racinej@mcmaster.ca}{racinej@mcmaster.ca}). And, of
course, if you encounter an issue that you think might be of interest
to others, kindly email me the relevant information and I will
incorporate it into this FAQ.

This FAQ refers to the most recent version, which as of this writing
is 0.60-20. Kindly update your version should you not be using the most
current (from within R, \texttt{update.packages()} ought to do it,
though also see \ref{update} below.). See the appendix in this file
for cumulative changes between this and previous versions of the
\texttt{np} package.

\section{Frequently Asked Questions}

\subsection{How do I cite the \texttt{np} package?}

Once you have installed the \texttt{np} package
(\texttt{install.packages("np")}), if you load the \texttt{np} package
(\texttt{library("np")}) and type \texttt{citation("np")}
you will be presented with the following information.

  \begin{singlespacing}
\begin{verbatim}
> citation("np")

To cite np in publications use:

  Tristen Hayfield and Jeffrey S. Racine (2008). Nonparametric Econometrics: The
  np Package. Journal of Statistical Software 27(5). DOI 10.18637/jss.v027.i05

A BibTeX entry for LaTeX users is

  @Article{,
    title = {Nonparametric Econometrics: The np Package},
    author = {Tristen Hayfield and Jeffrey S. Racine},
    journal = {Journal of Statistical Software},
    year = {2008},
    volume = {27},
    number = {5},
    url = {https://www.jstatsoft.org/index.php/jss/article/view/v027i05},
    doi = {10.18637/jss.v027.i05},
    pages = {1-32},
  }

\end{verbatim}
  \end{singlespacing}

\subsection{I have never used \texttt{R} before. Can you direct me to some
    introductory material that will guide me through the basics?}

  There are many excellent introductions to the \texttt{R} environment
  with more on the way. First, I would recommend going directly to the
  \texttt{R} website (\url{https://www.r-project.org}) and looking under
  Documentation/Manuals (\url{https://cran.r-project.org/manuals.html})
  where you will discover a wealth of documentation for \texttt{R} users
  of all levels. See also the \texttt{R} task views summary page
  (\url{https://cran.r-project.org/web/views/}) for
  information grouped under field of interest. A few documents that I
  mention to my students which are tailored to econometricians include
  \url{https://cran.r-project.org/doc/contrib/Verzani-SimpleR.pdf},
  Cribari-Neto \& Zarkos (1999) \cite{CRIBARI_NETO_ZARKOS:1999},
  Racine \& Hyndman (2002) \cite{RACINE_HYNDMAN:2002} and Farnsworth
  (2006) \cite{FARNSWORTH:2006}, to name but a few.

  Those looking for exemplar data sets outside of those contained in
  the \texttt{np} package are directed to the \texttt{Ecdat} \cite{Ecdat}
  and \texttt{AER} \cite{AER} packages.

  I maintain a 'Gallery' to provide a forum for users to share code
  and discover examples and illustrations which can be found at
  \url{https://jeffreyracine.github.io/gallery/}.

  Often the best resource is right down the hall. Ask a colleague
  whether they use or know anyone who uses R, then offer to buy that
  person a coffee and along the way drop something like ``I keep
  hearing about the \texttt{R} project\dots I feel like such a
  Luddite\dots''

  \subsection{\label{update}How do I keep all \texttt{R} packages on my
    system current?}

  Run the command \texttt{update.packages(checkBuilt=TRUE,ask=FALSE)},
  which will not only update all packages that are no longer current,
  but will also update all packages built under outdated installed
  versions of R, if appropriate.

\subsection{It seems that there are a lot of packages that must be
    installed in order to conduct econometric analysis (tseries,
    lmtest, np, etc.). Is there a way to avoid having to individually
    install each package individually?}

  Certainly. The Comprehensive R Archive Network (CRAN) is a network
  of ftp and web servers around the world that store identical,
  up-to-date, versions of code and documentation for \texttt{R}.  The
  CRAN 'task view' for computational econometrics might be of
  particular interest to econometricians.  The econometric task view
  provides an excellent summary of both parametric and nonparametric
  econometric packages that exist for the R environment and provides
  one-stop installation for these packages.

See
\href{https://CRAN.R-project.org/view=Econometrics}{https://CRAN.R-project.org/view=Econometricsl} for further information.


To automatically install a task view, the \texttt{ctv} package first
needs to be installed and loaded, i.e.,
\begin{verbatim}
install.packages("ctv")
library("ctv")
\end{verbatim}

The econometric task view can then be installed via
\texttt{install.views()} and updated via \texttt{update.views()}
(which first assesses which of the packages are already installed and
up-to-date), i.e.,
\begin{verbatim}
install.views("Econometrics")
\end{verbatim}
or
\begin{verbatim}
update.views("Econometrics")
\end{verbatim}

\subsection{Is there a 'gentle guide' to the \texttt{np} package that
    contains some easy to follow examples?}

  Perhaps the most gentle introduction is contained in the \texttt{np}
  package itself in the form of a 'vignette'. To view the vignette run
  R, install the \texttt{np} package (\texttt{install.packages("np")}), then
  type \texttt{vignette("np",package="np")} to view or print the vignette
  (this vignette is essentially the article that appeared in the
  Journal of Statistical Software that describes the \texttt{np} package
  (Hayfield \& Racine \cite{HAYFIELD_RACINE:2008})).

  See also \texttt{vignette("entropy\_np",package="np")} for a
  vignette on the entropy-based functions and procedures introduced to
  the \texttt{np} package in versions 0.30-4 through 0.30-8.

  In addition, you might be interested in the nonparametric
  econometrics primer (Racine \cite{RACINE:2008}) which is available
  for download from my website as is the code that will generate the
  examples contained therein.

  For a listing of all routines in the \texttt{np} package type:
  \texttt{library(help="np")}.

\subsection{I noticed you have placed a new version of the \texttt{np}
    package on CRAN. How can I determine what has been changed,
    modified, fixed etc?}

  See the CHANGELOG on the CRAN site
  (\url{https://CRAN.R-project.org/package=np/ChangeLog}), or go
  to the end of this document where the CHANGELOG is provided for your
  convenience.

\subsection{What is the difference between the \texttt{np} package and the
    previous stand-alone programs you wrote, namely, N \copyright,
    NPREG \copyright, and NPDEN \copyright?}

  The \texttt{np} package is built from the same C library that underlies
  its predecessors N \copyright, NPREG \copyright, and NPDEN
  \copyright. In fact, \texttt{R} calls the compiled C code that
  underlies its predecessors (one of the beauties of \texttt{R} is that
  you can obtain the benefits of compiled code (i.e., speed) yet have
  access to the rich superset of \texttt{R} routines and \texttt{R} packages
  built by others). Therefore, there is no penalty in run-time when
  using R versus the stand alone precompiled binary programs N
  \copyright, NPREG \copyright, and NPDEN \copyright\, (unless of
  course the compiler or compiler flags differ from those used to
  build its predecessors).

\subsection{How can I read data stored in various formats such as
    Stata, SAS, Minitab, SPSS etc.~into the R program?}

  Install the foreign library via \texttt{install.packages("foreign")}
  then do something like
  \begin{singlespacing}
\begin{verbatim}
mydat <- read.dta("datafile.dta"),
\end{verbatim}
  \end{singlespacing}
  where \texttt{datafile.dta} is the name of your Stata data
  file. Note that, as of version 0.8-34, the foreign package function
  \texttt{read.dta} supports reading files directly over the Internet
  making for more portable code. For instance, one could do something
  like
\begin{verbatim}
mydat <- read.dta(file="http://www.principlesofeconometrics.com/stata/mroz.dta")
\end{verbatim}
as one could always do with, say, \texttt{read.table()}.

\subsection{I want to use so-and-so's semiparametric/nonparametric
    method, however, the \texttt{np} package does not include this
    particular method\dots}

  This is why we have included the function \texttt{npksum()}, which
  exists so that you can create your own kernel objects and take
  advantage of underlying kernel methods implemented in the \texttt{np}
  package without having to write, say, C or Fortran code.

  With the options available, you could create new nonparametric tests
  or even new kernel estimators. For instance, the convolution kernel
  option would allow you to replicate, say, the least squares
  cross-validation function for kernel density estimation found in
  \texttt{npudensbw()}. The function \texttt{npksum()} uses highly-optimized
  C code that strives to minimize its memory footprint, while there is
  low overhead involved when using repeated calls to this function.

  See, by way of illustration, the example in the \texttt{npksum()}
  help file that conducts leave-one-out cross-validation for a local
  constant regression estimator via calls to the \texttt{R} function
  \texttt{nlm()}, and compares this to the \texttt{npregbw()}
  function.

  If you wish to have a method incorporated into a future version of
  the \texttt{np} package, the best way to achieve this is to
  successfully code up the method using \texttt{npksum()}, briefly
  document it and write up an example, then send it to us. We will
  then, at our discretion, do our best to adapt and incorporate this
  into a future version and of course give credit where credit is due.

\subsection{Cross-validation takes forever, and I can't wait that
    long\dots}

  This is the most common complaint from frustrated users coming to
  terms with numerically demanding statistical methods.  I am fond of
  saying 'if you want the wrong answer, I can give it to you right
  away', but this wears thin quickly.

  \begin{enumerate}

  \item Some background may be in order.  Suppose, by way of
    illustration, that you are conducting nonparametric regression
    (local constant or local linear) for a \textsl{given} bandwidth
    vector (nonparametric kernel regression is simply locally weighted
    least squares estimation). Let $g(x)$ denote the true conditional
    mean at some point $x$, and $\hat g(x)$ some estimate. To solve
    this problem requires computing weighted least squares not once
    (as would be the case for parametric regression), but $n$ times
    (the weights are local to the point at which you construct the
    regression model, $x_i$, $i=1,\dots,n$). That is, to compute
    $\hat g(x_i)$, $i=1,\dots,n$ requires an order of magnitude
    ($O(n)$) times more computation than that for parametric
    regression. So, for a \textsl{given} bandwidth, we require $O(n)$
    more computation than parametric regression. But to determine the
    appropriate bandwidth vector, we minimize, say, a cross-validation
    function numerically, which requires a large number of evaluations
    of some objective function, say the delete-one least squares
    criterion function $CV=n^{-1}\sum_{i=1}^n(y_i-\hat g_{-i}(x_i))^2$
    where $\hat g_{-i}(x_i)$ is the leave-one-out estimator of
    $g(x_i)$. This takes a problem that is already an order of
    magnitude more computationally involved than parametric regression
    and again increases the computational burden by potentially
    another order of magnitude. It is evident that as $n$ increases
    the computational burden associated with optimal bandwidth
    selection will increase exponentially.

    In general, cross-validation methods have run times that are
    proportional to the square of the number of observations (of
    computational order $n^2$ hence a doubling of the sample size will
    increase run time by a factor of four). The solution I currently
    favor is to run the code in a parallel computing environment. The
    underlying C code for \texttt{np} is MPI-aware (MPI denotes the
    'message passing interface', a popular parallel programming
    library that is an international standard), and a version of the
    \texttt{np} package titled '\texttt{npRmpi}' exists for running
    jobs in a parallel environment that leverages the \texttt{Rmpi}
    package (\cite{Rmpi}).\footnote{We are extremely grateful to Hao
      Yu for providing the MPI functionality contained in the
      \texttt{Rmpi} package.}

    With respect to the \texttt{npRmpi} package, kindly note that I
    cannot assist with issues surrounding installation and setup due
    to the vast heterogeneity of MPI implementations and methods for
    executing such programs. You are instead strongly advised to seek
    local advice from your sysadmin or others. The document
    \texttt{npRmpi.pdf} may contain some useful information for such
    issues. You might also want to first get the \texttt{Rmpi} package
    installed and running properly as once you are at this stage it
    ought to then be trivial to install the \texttt{npRmpi}
    package. Also note that running programs in a parallel environment
    requires minor differences in how \texttt{np} functions are
    called, and you would be wise to examine the examples in the demo
    directory (download and unpack the source code and look in this
    directory) and the overview file \texttt{npRmpi.pdf} in the
    inst/doc/ directory of the \texttt{npRmpi} package you downloaded
    and unpacked.

  \item Alternatively, you can use the method outlined in Racine
    (1993) \cite{RACINE:1993}. The method is based on the fact that
    the unknown constant $c_j$ (the 'scale factor') in the formula
    $c_j\sigma_j n^{-1/(2p+r)}$ is independent of the sample size, so
    one can conduct bandwidth selection on random subsets and do this
    for a large number of subsets then take the mean/median over these
    subsets and feed the scale factor into the final routine for the
    entire sample. Below you will find simple \texttt{R} code that
    replicates the method using numerical search and resampling
    without replacement rather than the grid method outlined in
    \cite{RACINE:1993} (both have equivalent properties but this is
    perhaps simpler to implement using the \texttt{np} package).

    \begin{singlespacing}
\begin{verbatim}
## Regression example
## Generate a moderately large data set

set.seed(12345)
n <- 100000
x1 <- runif(n)
x2 <- runif(n)

y <- 1 + x1 + sin(pi*x2) + rnorm(n,sd=.1)

## Set the number of resamples and the subsample size

num.res <- 50
n.sub <- 250

## Create a storage matrix

bw.mat <- matrix(NA,nrow=num.res,ncol=2)

## Get the scale factors for resamples from the full sample of size n.sub

options(np.messages=FALSE)

for(i in 1:num.res)  {

  cat(paste(" Replication", i, "of", num.res, "...\r"))

  bw.mat[i,] <- npregbw(y~x1+x2,regtype="ll",
                        subset=sample(n,n.sub))$sfactor$x

}

## A function to compute the median of the columns of a matrix

colMedians <- function(data) {
  colmed <- numeric(ncol(data))
  for(i in 1:ncol(data)) {
    colmed[i] <- median(data[,i])
  }
  return(colmed)
}

## Take the median scale factors

bw <- colMedians(bw.mat)

## The final model for the full dataset

model.res <- npreg(y~x1+x2,bws=bw,regtype="ll",bwscaling=TRUE)
\end{verbatim}
    \end{singlespacing}

\begin{singlespacing}
\begin{verbatim}
## Hat tip to Yoshi Fujiwara <yoshi.fujiwara@gmail.com> for this 
## nice example

n <- 100000

library(MASS)
rho <- 0.25
Sigma <- matrix(c(1,rho,rho,1),2,2)
mydat <- mvrnorm(n=n, rep(0, 2), Sigma)
x <- mydat[,1]
y <- mydat[,2]
rm(mydat)

num.res <- 100
n.sub <- 100

bw.mat <- matrix(NA,nrow=num.res,ncol=2)
options(np.messages=FALSE)
for(i in 1:num.res) {
  bw <- npcdensbw(y ~ x,subset=sample(n,n.sub))
  bw.mat[i,] <- c(bw$sfactor$y,bw$sfactor$x)
}

colMedians <- function(data) {
 colmed <- numeric(ncol(data))
 for(i in 1:ncol(data)) {
   colmed[i] <- median(data[,i])
 }
 return(colmed)
}

bw <- colMedians(bw.mat)
bw <- npcdensbw(y ~ x, bws=bw, bwscaling=TRUE, bandwidth.compute=FALSE)
summary(bw)
plot(bw,xtrim=.01)
\end{verbatim}
\end{singlespacing}

\item Barring this, you can set the search tolerances to be a bit less
  terse (at the expense of potential accuracy, i.e., becoming trapped
  in local minima) by setting, say, \texttt{tol=0.1} and
  \texttt{ftol=0.1} in the respective bandwidth routine (see the docs
  for examples). Also, you can set \texttt{nmulti=1} which overrides
  the number of times the search procedure restarts from different
  random starting values (the default is to restart $k$ times where
  $k$ is the number of variables). Be warned, however, that this is
  {\em definitely not recommended} and should {\em be avoided at all
    costs} for all but the most casual examination of a
  relationship. One ought to use multistarting for any final results
  and never override default search tolerances {\em unless increasing
    multistarts beyond the default}. Results based upon exhaustive
  search {\em often differ dramatically} from that based on limited
  search achieved by overriding default search tolerances.

  \item For those who like to tinker and who work on a *NIX system
    with the gcc compiler suite, you can change the default compiler
    switches used for building \texttt{R} packages which may generate
    some modest improvements in run time. The default compiler
    switches are
    \begin{singlespacing}
\begin{verbatim}
 -g -O2
\end{verbatim}
    \end{singlespacing}
    and are set in the R-*.*.*/etc/Makeconf file (where *.*.* refers
    to your \texttt{R} version number, e.g. R-2.10.1).  You can edit this
    file and change these defaults to
    \begin{singlespacing}
\begin{verbatim}
-O3 -ffast-math -fexpensive-optimizations -fomit-frame-pointer
\end{verbatim}
    \end{singlespacing}
    then reinstall the \texttt{np} package and you may experience some
    improvements in run time. Note that the -g flag turns on
    production of debugging information which can involve some
    overhead, so we are disabling this feature. This is not a feature
    used by the typical applied researcher but if you envision
    requiring this it is clearly trivial to re-enable debugging. I
    typically experience in the neighborhood of a 0-5\% reduction in
    run time for data-driven bandwidth selection on a variety of
    systems depending on the method being used, though mileage will of
    course vary.

  \item Finally, I have recently been working on extending regression
    splines (as opposed to smoothing splines\footnote{Unlike
      regression splines, a smoothing spline places a knot at each
      data point and penalizes the fit for lack of smoothness as
      defined by the second derivative (typically cubic splines are
      used). When the penalty is zero this produces a function that
      interpolates the data points. When the penalty is infinite, this
      delivers the linear OLS fit to the data.}) to admit categorical
    predictors (see references for papers with Yang and Ma in the
    \texttt{crs} package). Because regression splines involve simple
    (i.e., 'global' as opposed to local) least-squares fits, they
    scale much better with respect to the sample size so for large
    sample sizes you may wish to instead consider this approach
    (kindly see my webpage for further details). You can run
    cross-validation with hundreds of thousands of observations on a
    decent desktop in far less time than that required for
    cross-validated kernel estimates. Be forewarned, however, that the
    presence of categorical predictors can lead to increased execution
    time unless the option \texttt{kernel=FALSE} is invoked (the
    default is to use local kernel weighting in the presence of
    categorical predictors).

  \end{enumerate}

\subsection{Is
    there a way to figure out roughly how long
    cross-validation will take on a large sample?}

  Certainly. You can run cross-validation on subsets of your data of
  increasing size and time each run, then estimate a double-log model
  of sample size on run time (run time can be approximated by a linear
  log-log model) and then use this to predict approximate
  run-time. The following example demonstrates this for a simple
  model, but you can modify it trivially for your data. Note that the
  larger is \texttt{n.max} the more accurate it will likely be. Note that
  we presume your data is in no particular order (if it is, you
  perhaps ought to shuffle it first). We plot the log-log model fit
  and prediction along with that expressed in hours.

  \begin{singlespacing}
\begin{verbatim}
## Set the upper bound (n.max > 100) for the sub-samples on which you 
## will run cross-validation (perhaps n.max = 1000 (or 2000) ought to 
## suffice). For your application, n will be your sample size

n <- 2000
n.max <- 1000

x <- runif(n)
y <- 1 + x + rnorm(n)

n.seq <- seq(100,n.max,by=100)
time.seq <- numeric(length(n.seq))

for(i in 1:length(n.seq)) {
  time.seq[i] <- system.time(npregbw(y~x,subset=seq(1:n.seq[i])))[3]
}

## Now fit a double-log model and generate/plot actual values plus
## prediction for n (i.e., approximate run time in hours)

log.time <- log(time.seq)
log.n <- log(n.seq)

model <- lm(log.time~log.n)

n.seq.aug <- c(n.seq,n)
time.fcst <- exp(predict(model,newdata=data.frame(log.n=log(n.seq.aug))))

par(mfrow=c(2,1))

plot(log(n.seq.aug),log(time.fcst),type="b",
     xlab="log(Sample Size)",
     ylab="log(Run Time)",
     main="Approximate Run Time (log seconds)")

plot(n.seq.aug,time.fcst/3600,type="b",
     xlab="Sample Size (n)",
     ylab="Hours",
     main="Approximate Run Time (hours)",
     sub=paste("Predicted run time for n =", n, "observations:",
     signif(time.fcst[length(time.fcst)]/3600, digits=2),
     "hours"))
\end{verbatim}
  \end{singlespacing}

\subsection{Where can I get some examples of R code for the np
  package in addition to the examples in the help files?}

Start \texttt{R} then type \verb+demo(package="np")+ and you will be
presented with a list of demos for constrained estimation, inference,
and so forth. To run one of these demos type, for example,
\verb+demo(npregiv)+ (note that you must first install the \texttt{rgl} package to run this particular demo).

To find the location of a demo type
\verb+system.file("demo","npregiv.R",package="np")+ for example,
then you can take the source code for this demo and modify it for your
particular application.

You can also find examples and illustrations at the 'Gallery' located
at \url{https://jeffreyracine.github.io/gallery/}.

\subsection{I need to apply a boundary correction for a univariate
  density estimate - how can I do this?}

As of version 0.60.5, you can use either \texttt{npuniden.boundary}
(boundary kernel functions) or \texttt{npuniden.reflect} (data
reflection).

\subsection{I notice your density estimator supports manual bandwidths,
    the normal-reference rule-of-thumb, likelihood cross-validation
    and least squares cross-validation, but not plug-in rules. How can
    I use various plug-in rules for estimating a univariate density?}

  For the univariate case this is straightforward as the default R
  installation supports a variety of univariate plug-in bandwidths
  (see \texttt{?bw.nrd} for details). For example, \texttt{bs.SJ} computes
  the bandwidths outlined in

\begin{verbatim}
     Sheather, S. J. and Jones, M. C. (1991) A reliable data-based
     bandwidth selection method for kernel density estimation.
     _Journal of the Royal Statistical Society series B_, *53*,
     683-690.
\end{verbatim}

  Incorporating these univariate plug-in bandwidth selectors into the
  univariate density estimation routines in \texttt{np} is
  straightforward as the following code snippet demonstrates. They
  will certainly be faster than the likelihood and least-squares
  cross-validation approaches. Also, you may not wish the density
  estimate for all sample realizations, but rather for a shorter
  grid. The following example demonstrates both and is closer in
  spirit to the \texttt{density()} function in base R.

\begin{verbatim}
x <- rnorm(10000)
xeval <- seq(min(x),max(x),length=100)
f <- npudens(tdat=x,edat=xeval,bws=bw.SJ(x))
\end{verbatim}

  You might even be tempted to use these in the multivariate case via
  \texttt{bws=c(bw.SJ(x1),bw.SJ(x2),...)} though these would be optimal
  for univariate densities and most certainly not for a multivariate
  density. However, for exploratory purposes these may be of interest
  to some users.

\subsection{\label{code_nowork}I wrote a program using \texttt{np} and it
    does not work as I expected\dots}

  There exist a rather extensive set of examples contained in the
  docs. You can run these examples by typing
  \texttt{example("npfunctionname")} where npfunctionname is, say,
  \texttt{w}, as in \texttt{example("w")}.\footnote{For a listing of
    all routines in the np package type: \texttt{library(help="np")}.}
  These examples all pass quality control and produce the expected
  results, so first see whether your problem fits into an existing
  example, and if not, carefully follow the examples listed in a given
  function for syntax issues etc.

  If you are convinced that the problem lies with \texttt{np} (there
  certainly will be undiscovered 'features', i.e., bugs), then kindly
  send me your code and data so that I can replicate and help resolve
  the issue.

\subsection{Under Mac OS X, when I run a command no progress is
    displayed\dots}

  This should no longer occur for np versions 0.30-0 and up. For
  previous versions, this reflected a peculiarity of console
  input/output (I/O) under Mac OS X.  Note, however, that if you run {
    \tt R} in a terminal rather than \texttt{Rgui} you will get the full
  *NIX\footnote{*NIX is often used to describe UNIX and other
    UNIX-like platforms (i.e., UNIX, BSD, and GNU/Linux
    distributions). I harbour strong preferences for *NIX computing
    platforms.}  experience. 

  But also note that there is a platform-independent interface that
  does not suffer from this limitation called 'RStudio' that you might
  prefer to existing interfaces (\url{https://posit.co/}).

\subsection{When some routines are running under MS Windows, \texttt{R}
    appears to be 'not responding.' It appears that the program is not
    'hung', rather is simply computing. The previous stand-alone
    program (N \copyright) always displayed useful information\dots}

  This should no longer occur for np versions 0.30-0 and up. For
  previous versions, this reflected a peculiarity of the R Windows
  GUI, and was not specific to the \texttt{np} package.

  From the \texttt{R} Windows FAQ\dots

  ``When using Rgui the output to the console seems to be delayed.
  This is deliberate: the console output is buffered and re-written in
  chunks to be faster and less distracting. You can turn buffering off
  or on from the 'Misc' menu or the right-click menu: \verb+<Ctrl-W>+
  toggles the setting.''

\subsection{Some results take a while, and my MS Windows computer is
    sluggish while \texttt{R} is running\dots}

  You can easily change the priority of your \texttt{R} job on the
  fly, just as you might under *NIX.  Pull up the task manager
  (\verb+<Ctrl>-<Alt>-<Del>+), go to the process list, and find the
  process \texttt{Rgui.exe} (or \texttt{R.exe} if you are running
  \texttt{Rterm}), select this process by left clicking on it, then
  right clicking will bring up a menu, select \texttt{Set priority},
  then change priority to \texttt{low} and hit $<$\texttt{ok}$>$. For
  lengthy jobs this will make your life much smoother, and you can,
  say, run multiple jobs in low priority with no sluggishness
  whatsoever for your other applications (useful for queuing a number
  of long jobs). Alternatively, you could permanently change the
  default priority of \texttt{R} under MS Windows by modifying the
  properties of your \texttt{R} desktop icon.

\subsection{\label{factor}A variable must be cast as, say, a factor in
    order for \texttt{np} to recognize this as an unordered factor. How
    can I determine whether my data is already cast as a factor?}

  Use the \texttt{class()} function. For example, define \texttt{x <-
    factor(c("male","female"))}, then type \texttt{class(x)}.

\subsection{When I use \texttt{plot()} \texttt{(npplot())} existing graphics
    windows are overwritten. How can I display multiple graphics plots
    in separate graphics windows so that I can see results from
    previous runs and compare that to my new run?}

  Use the \texttt{dev.new()} command in between each call to \texttt{plot()}. This will leave the existing graphics window open and
  start a new one. The command \texttt{dev.list()} will list all graphics
  windows, and the command \texttt{dev.set(integer.foo)} will allow you
  to switch from one to another and overwrite existing graphics
  windows should you so choose.

  Alternately, you can use RStudio (\url{https://posit.co/})
  where the plot window is such that previous plots can be recalled on
  the fly, resized, saved in various formats etc.

\subsection{\label{plot names}Sometimes \texttt{plot()} fails to use my
    variable names\dots}

  This should not occur unless you are using the data frame method and
  not naming your variables (e.g., you are doing something like
  data.frame(ordered(year))). To correct this, name your variables in
  the respective data frame, as in

  \texttt{data <- data.frame(year=ordered(year),gdp)}

  \noindent so that the ordered factor appears as 'year' and not
  'ordered.year'

\subsection{Sometimes \texttt{plot()} appends my variable names with
    .ordered or .factor\dots}

  See also \ref{plot names} above.

\subsection{I specify a variable as \texttt{factor()} or \texttt{ordered()}
    in a data frame, then call this when I conduct bandwidth
    selection. However, when I try to plot the resulting object, it
    complains with the following message:}

    \texttt{Error in eval(expr, envir, enclos) : object ``variable'' not
      found\dots}

  This arises because \texttt{plot()} (\texttt{npplot()}) tries to retrieve
  the variable from the environment but you have changed the
  definition when you called the bandwidth selection routine (e.g.,
  \texttt{npregbw(y\textasciitilde x,data=dataframe)}).

  To correct this, simply call \texttt{plot()} with the argument
  \texttt{data=dataframe} where \texttt{dataframe} is the name of your
  data frame.

\subsection{My \texttt{np} code produces errors when I attempt to run
    it\dots}

  First, it is good practice to name all arguments (see the docs for
  examples) as in \texttt{npregbw(formula=y\textasciitilde x)} (i.e.,
  explicitly call formula for functions that use named formulas). This
  will help the code return a potentially helpful error message.

  Next, follow the examples listed at the end of each function help
  page closely (i.e., \texttt{?npreg} then scroll down to
  \texttt{Examples:}). See also \ref{code_nowork} above.

\subsection{\label{0/1}I have (numeric) 0/1 dummy variable regressors
    in my parametric model. Can I just pass them to the \texttt{np}
    functions as I would in a parametric setting?}

  In general, definitely not -- you need to correctly classify each
  variable as type \texttt{factor} and treat it as one variable only. By
  way of example, suppose in your data you have created dummy
  variables for year, for example, dummy06 which equals 1 for 2006, 0
  otherwise, dummy07 which equals 1 for 2007, 0 otherwise etc. We
  create these by habit for parametric models. But, the underlying
  variable is simply year, which equals 2006, 2007, and so forth.

  In \texttt{np} (and \texttt{R} in general), you get to economize by
  just telling the function that the variable 'year' is ordered, as in
  ordered(year), where year is a vector containing elements 2006, 2007
  etc. Of course, seasoned R users would appreciate that this is in
  fact the simple way to do it with a parametric model as well.

  You would {\em never}, therefore, just pass dummy variables to an
  \texttt{np} function as you would for linear parametric models. The
  {\em only} exception is where you have only one 0/1 dummy for one
  variable, say '\texttt{sex}', and in this case you still would have
  to enter this as \texttt{factor(sex)} so that the \texttt{np}
  function recognizes this as a factor (otherwise it would treat it as
  continuous and use a kernel function that is inappropriate for a
  factor).

\subsection{\label{terminates}I have a categorical variable, ignored
    the advice in items \ref{factor} and \ref{0/1}, and R terminates
    with the following error.}

\begin{verbatim}
 ** Fatal Error in routine kernel_bandwidth() ** variable 0 appears to be constant!
 ** Program terminated abnormally!
\end{verbatim}

  Presuming your variable is not in fact a constant (i.e., is not in
  fact a 'variable'), this can only occur in the case where a variable
  is 'pathological' in that it has \texttt{IQR=0} but \texttt{std>0}
  (see the section titled 'Changes from Version 0.30-1 to 0.30-2
  [19-Apr-2009]' for further details).  This should no longer occur
  for np versions 0.30-2 and up.

\subsection{Rgui appears to crash. There must be a bug in the program.}

  Try running your code using the terminal (i.e., \texttt{Rterm} in
  Windows or \texttt{R} in a Mac OS X terminal) and see whether you get
  the message in item \ref{terminates}.

\subsection{Can I skip creating a bandwidth object and enter a
    bandwidth directly?}

  Certainly, though I would advise doing so for exploratory data
  analysis only.  For example, attach a dataset via
  \begin{singlespacing}
\begin{verbatim}
data(cps71)
attach(cps71)
\end{verbatim}
  \end{singlespacing}
  then enter, say,
  \begin{singlespacing}
\begin{verbatim}
plot(age,logwage,main="Manual Bandwidth Example")
lines(age,fitted(npreg(logwage~age,bws=1)),col="blue",lty=1)
lines(age,fitted(npreg(logwage~age,bws=2)),col="red",lty=2)
lines(age,fitted(npreg(logwage~age,bws=3)),col="green",lty=3)
legend(20,15,
       c("h=1","h=2","h=3"),
       col=c("blue","red","green"),
       lty=c(1,2,3))
\end{verbatim}
  \end{singlespacing}
  to plot the local constant estimator with bandwidths of 1, 2, and 3
  years. Note that the age variable is already sorted in this
  dataset. If your data is not sorted you will need to do so prior to
  plotting so that your \texttt{lines} command works properly. Or see
  \ref{partial grad q} below for a multivariate example.

\subsection{\label{partial grad q}When I estimate my gradients and
    there are two or more covariates and then extract them with the
    \texttt{gradients()} function, they are not 'smooth', though if I
    plot a model with the \texttt{gradients=TRUE} option, they are. The
    \texttt{gradients()} function must be broken\dots}

  The function \texttt{plot()} (\texttt{npplot()}) plots 'partial'
  means and gradients. In other words, it plots $x_1$ versus $\hat
  g(x_1,\bar x_2)$ for the partial mean, where $\bar x_2$ is, say, the
  median/modal value of $x_2$. It also plots $x_1$ versus
  $\partial\hat g(x_1,\bar x_2)/\partial x_1$ for the gradient. Note
  that we are controlling for the values of the other
  covariate(s). This is in effect what people expect when they play
  with linear parametric models of the form $y=\beta_0+\beta_1
  x_1+\beta_2x_2+\epsilon$ since, given the additive nature of the
  model, $\partial y/\partial x_1=\beta_1$ (i.e., does not vary with
  $x_2$).

  The example below shows how you could manually generate the partial
  gradients (and means) for your data where the sample realizations
  form the evaluation data for $x_1$ (unlike \texttt{npplot()} which
  uses an evenly spaced grid). Note we use the function
  \texttt{uocquantile()} to generate a vector that holds $x_2$
  constant at is median/modal value (i.e., the 0.5 quantile) in the
  evaluation data. The function \texttt{uocquantile()} can compute
  quantiles for ordered, unordered, and continuous data (see
  \texttt{?uocquantile} for details).

\begin{singlespacing}
\begin{verbatim}
n <- 100

x1 <- runif(n)
x2 <- runif(n)
y <- x1^2+x2^2 + rnorm(n,sd=.1)

data.train <- data.frame(x1,x2,y)

bw <- npregbw(y~x1+x2,
              data=data.train,
              regtype="ll",
              bwmethod="cv.aic")

data.eval <-  data.frame(x1 = sort(x1),
                    x2 = rep(uocquantile(x2,.5),n))

model <- npreg(bws=bw,
               data=data.train, 
               newdata=data.eval,
               gradients=TRUE)

plot(data.eval[,1],model$grad[,1],xlab="X1",ylab="Gradient",type="l")
\end{verbatim}
\end{singlespacing}

Note that this uses the sorted sample realizations for \texttt{x1}
which is perfectly acceptable. If you want to mimic \texttt{plot()}
exactly you will see that by default plot uses a grid of equally
spaced values of length \texttt{neval=50} as per below. Both are
perfectly acceptable and the point is they control for the level of
the non-axis variables.
\begin{singlespacing}
\begin{verbatim} 
data.eval <-  data.frame(x1 = seq(min(x1),max(x1),length=50),
                         x2 = rep(uocquantile(x2,.5),50))  
\end{verbatim}
\end{singlespacing}

\subsection{I use \texttt{plot()} \texttt{(npplot())} to plot, say, a density
    and the resulting plot looks like an inverted density rather than
    a density\dots}

  This can occur when the data-driven bandwidth is dramatically
  undersmoothed. Data-driven (i.e., automatic) bandwidth selection
  procedures are not guaranteed always to produce good results due to
  perhaps the presence of outliers or the rounding/discretization of
  continuous data, among others. By default, \texttt{npplot()} takes
  the two extremes of the data (minimum, maximum i.e., actual data
  points) then creates an equally spaced grid of evaluation data
  (i.e., not actual data points in general) and computes the density
  for these points. Since the bandwidth is extremely small, the
  density estimate at these evaluation points is correctly zero, while
  those for the sample realizations (in this case only two, the min
  and max) are non-zero, hence we get two peaks at the edges of the
  plot and a flat bowl equal to zero everywhere else.

  This can also happen when your data is heavily discretized and you
  treat it as continuous. In such cases, treating the data as ordered
  may result in more sensible estimates.

\subsection{Can \texttt{npksum()} compute analytical derivatives with
    respect to a continuous variable?}

  As of version 0.20-0 and up, yes it can, using the \texttt{operator
    = "derivative"} argument, which is put to its paces in the
  following code snippet (this supports multiple arguments including
  \texttt{"integral"} and \texttt{"convolution"} in addition to
  \texttt{"normal"}, the default).

  \begin{singlespacing}
\begin{verbatim}
Z <- seq(-2.23,2.23,length=100)
Zc <- seq(-4.47,4.47,length=100)

par(mfrow=c(2,2))

plot(Z,main="Kernel",ylab="K()",npksum(txdat=0,exdat=Z,bws=1,
         ckertype="epanechnikov",ckerorder=2,operator="normal")$ksum,
         col="blue",type="l")

plot(Z,main="Kernel Derivative",ylab="K()",npksum(txdat=0,exdat=Z,bws=1,
         ckertype="epanechnikov",ckerorder=2,operator="derivative")$ksum,
         col="blue",type="l")

plot(Z,main="Kernel Integral",ylab="K()",npksum(txdat=0,exdat=Z,bws=1,
         ckertype="epanechnikov",ckerorder=2,operator="integral")$ksum,
         col="blue",type="l")

plot(Zc,main="Kernel Convolution",ylab="K()",npksum(txdat=0,exdat=Zc,bws=1,
         ckertype="epanechnikov",ckerorder=2,operator="convolution")$ksum,
         col="blue",type="l")
\end{verbatim}
  \end{singlespacing}

  An alternative to computing analytical derivatives is to compute
  them numerically using finite-differences. One simply computes the
  kernel sum evaluating the sum with variable $j$ set at $x_j-h_j/2$
  and calls this, say, $ksum_{j1}$, then again set at $x_j+h_j/2$ and
  call this $ksum_{j}2$, then compute
  $\nabla=(ksum_{j2}-ksum_{j1})/h_j$. This method has been used for
  both theoretical and applied work and produces consistent estimates
  of the derivatives, as of course do the analytical derivatives,
  providing that $h\to0$ as $n\to\infty$ (which will {\em not} be the
  case in some settings, i.e., in the presence of irrelevant
  covariates and so forth). The following example provides a simple
  demonstration. See \ref{partial grad q} above for multivariate
  partial regression when using this method.

  \begin{singlespacing}
    \begin{singlespacing}
\begin{verbatim}
## In this example we consider the local constant estimator computed
## using npksum, and then use npksum to compute numerical derivatives
## using finite-difference methods, then finally compare them with the
## analytical ones.

data(cps71)
attach(cps71)

## Grab the cross-validated bandwidth

bw <- npregbw(logwage~age)
h <- bw$bw[1]

## Evaluate the local constant regression at x-h/2, x+h/2...

ksum.1 <- npksum(txdat=age, exdat=age-h/2,tydat=logwage,bws=bw)$ksum/
  npksum(txdat=age,exdat=age-h/2,bws=bw)$ksum

ksum.2 <- npksum(txdat=age, exdat=age+h/2,tydat=logwage,bws=bw)$ksum/
  npksum(txdat=age,exdat=age+h/2,bws=bw)$ksum

## Compute the numerical gradient...

grad.numerical <- (ksum.2-ksum.1)/h

## Compare with the analytical gradient...

grad.analytical <- gradients(npreg(bws=bw,gradient=TRUE))

## Plot the resulting estimates...

plot(age,grad.numerical,type="l",col="blue",lty=1,ylab="gradient")
lines(age,grad.analytical,type="l",col="red",lty=2)
legend(20,-0.05,c("Numerical","Analytic"),col=c("blue","red"),lty=c(1,2))
\end{verbatim}
    \end{singlespacing}
  \end{singlespacing}

\subsection{Can I use the \texttt{npcmstest()} function that implements
    the consistent test for correct specification of parametric
    regression models as described in Hsiao, Li, \& Racine (2007)
    \cite{HSIAO_LI_RACINE:2007} to test for correct specification of
    the semiparametric partially linear model?}

  As Brennan Thompson points out, yes, you can.

  To test a parametric linear specification against a semiparametric
  partially linear alternative, i.e.,
  \begin{align*}
    H_0: y &= X'\beta + Z'\gamma + u\\
    H_1: y &= X'\beta + g(Z) + u,
  \end{align*}
  you could use \texttt{npcmstest()} as follows:
  \begin{singlespacing}
\begin{verbatim}
  lmodel <- lm(y~X+Z,y=TRUE,x=TRUE)
  uhat <- resid(lmodel)
  npcmstest(xdat=Z,ydat=uhat,model=lmodel)
\end{verbatim}
  \end{singlespacing}

  A slightly better way (as discussed in Li \& Wang (1998)
  \cite{LI_WANG:1998}) would be to use a 'mixed' residual, i.e., $\hat
  u_i = y_i - X_i'\tilde \beta - Z_i'\hat \gamma$ in the test, where
  $\tilde\beta$ is the semiparametric estimator of $\beta$ (based on
  the semiparametric partially linear model), and $\hat \gamma$ is the
  OLS estimator of $\gamma$ based on the linear model. This could lead
  to potential power gains due to the improved efficiency of
  $\hat\beta$ under the alternative.

\subsection{I am using \texttt{npcmstest()} on a \texttt{glm()} object (the
    document says glm() objects are supported and I am estimating a
    Logit model) but it returns an error saying}
\begin{verbatim}
 Error in eval(expr, envir, enclos) : y values must be 0 <= y <= 1.
\end{verbatim}

  \texttt{npcmstest()} supports conditional mean models with continuous
  outcomes (\texttt{glm()} objects are supported so that models that are
  nonlinear in parameters can be estimated). The test is based on
  residual bootstrapping to generate resamples for $Y$. In particular,
  a resample for the residual vector ($\hat\epsilon^*$) is added to
  the models' fit (i.e., $Y^*=\hat Y + \hat\epsilon^*$) to generate a
  resample under the null. This excludes binary outcome models and the
  like because you would have generated a resample for $Y$ that no
  longer contains zeros and ones, hence the error message.

  Note that \texttt{npcmstest} supports regression objects generated
  by \texttt{lm} and uses features specific to objects of type
  \texttt{lm} hence if you attempt to pass objects of a different type
  the function cannot be expected to work.

\subsection{I want to plot the kernel function itself. How can I do
    this?}

  Use the \texttt{npksum()} function and switch the evaluation and
  training roles as in the following example that plots the 2nd, 4th,
  6th and 8th order Epanechnikov kernels.
  \begin{singlespacing}
\begin{verbatim}
Z <- seq(-sqrt(5),sqrt(5),length=100)
par(mfrow=c(2,2))
plot(Z,ylab="kernel",npksum(txdat=0,exdat=Z,bws=1,ckertype="epanechnikov",
ckerorder=2)$ksum,type="l",main="Epanechnikov [order = 2]")
plot(Z,ylab="kernel",npksum(txdat=0,exdat=Z,bws=1,ckertype="epanechnikov",
ckerorder=4)$ksum,type="l",main="Epanechnikov [order = 4]")
plot(Z,ylab="kernel",npksum(txdat=0,exdat=Z,bws=1,ckertype="epanechnikov",
ckerorder=6)$ksum,type="l",main="Epanechnikov [order = 6]")
plot(Z,ylab="kernel",npksum(txdat=0,exdat=Z,bws=1,ckertype="epanechnikov",
ckerorder=8)$ksum,type="l",main="Epanechnikov [order = 8]")
\end{verbatim}
  \end{singlespacing}

\subsection{In version 0.20-0 and up I can 'combine' steps such as
    bandwidth selection and estimation. But when I do \texttt{summary(model)} I don't get the same summary that I would
    get from, say, \texttt{summary(bw)} and then \texttt{summary(model)}. How do I get bandwidth object summaries
    when combining steps?}

  Don't worry, the bandwidth object exists when you do the combined
  steps and is easily accessed via \texttt{summary(model\$bws)} or
  extracted via \texttt{bw <- model\$bws} where \texttt{model} is
  the name of your model.

\subsection{I estimated a semiparametric index model via \texttt{model <-
      npindex(y\textasciitilde x1+x2) } but \texttt{se(model)} returns NULL}.

  Perhaps you want \texttt{vcov(model)} instead (i.e., the asymptotic
  variance-covariance matrix)? This is supported as of version 0.40-1
  provided that you set \texttt{gradients=TRUE} as the following snippet
  demonstrates:
\begin{verbatim}
set.seed(42)
n <- 250
x1 <- runif(n, min=-1, max=1)
x2 <- runif(n, min=-1, max=1)
y <- ifelse(x1 + x2 + rnorm(n) > 0, 1, 0)
## Note that the first element of the vector beta is normalized to one
## for identification purposes hence the first row and column of the
## covariance matrix will contain zeros.
model <- npindex(y~x1+x2, method="kleinspady", gradients=TRUE)
vcov(model)
Z <- coef(model)[-1]/sqrt(diag(vcov(model)))[-1]
Z
\end{verbatim}

  Note that, alternatively, you can get robust bootstrapped standard
  errors for the estimated model and gradients by adding the argument
  \texttt{errors=TRUE} to your call to npindex so that
  \texttt{se(model)} returns the vector of standard errors for the
  estimated conditional mean where \texttt{model} is the name of your
  model.  Note that \texttt{model\$merr } will contain the standard
  errors returned by \texttt{se(model)} while \texttt{model\$gerr}
  will return the matrix of standard errors for the gradients {\em
    provided} you have set \texttt{gradients=TRUE} (furthermore,
  \texttt{model\$mean.grad} and \texttt{model\$mean.gerr} will give
  the average derivative and its bootstrapped standard errors). See
  the documentation of npindex for further details. The following code
  snippet demonstrates how one could do this for a simulated dataset.
\begin{verbatim}
  n <- 100
  x1 <- runif(n, min=-1, max=1)
  x2 <- runif(n, min=-1, max=1)
  y <- x1 - x2 + rnorm(n)

  bw <- npindexbw(formula=y~x1+x2)
  model <- npindex(bws=bw,errors=TRUE,gradients=TRUE)

  se.mean <- model$merr
  se.grad <- model$gerr
\end{verbatim}

\subsection{How do I interpret gradients from the conditional density
    estimator?}

  If you plot a conditional density $f(y|x)$ when $x$ is a scalar,
  with gradients, by default you will get the following:

  \begin{enumerate}

  \item A plot of $\partial f(y = \text{median} | x)/\partial x$
    (admittedly not the most useful plot).  (If $y$ is discrete the
    only difference is that you get a plot of $\partial f(y =
    \text{(unconditional) mode} | x)/\partial x$).

  \item A plot of $\partial f(y | x = \text{median})/\partial x$.

  \end{enumerate}

  If $x$ is multivariate (for example, 2D) you get:

  \begin{enumerate}

  \item A plot of $\partial f(y = \text{median} | x1, x2 =
    \text{median})/\partial x_1$
  \item A plot of $\partial f(y = \text{median} | x1, x2 =
    \text{median})/\partial x_2$

  \item A plot of $\partial f(y = \text{median} | x1 = \text{median},
    x2)/\partial x_1$
  \item A plot of $\partial f(y = \text{median} | x1 = \text{median},
    x2)/\partial x_2$

  \item A plot of $\partial f(y | x1 = \text{median}, x2 =
    \text{median})/\partial x_1$
  \item A plot of $\partial f(y | x1 = \text{median}, x2 =
    \text{median})/\partial x_2$

  \end{enumerate}

\subsection{When I run \texttt{R} in batch mode via \texttt{R CMD BATCH
      filename.R} unwanted status messages (e.g., ``Multistart 1 of
    10'') crowd out desired output. How can I turn off these unwanted
    status messages?}

  After loading the np library add the line
  \texttt{options(np.messages=FALSE)} and all such messages will be
  disabled.

\subsection{I am getting an 'unable to allocate...' message after
    repeatedly interrupting large jobs.}

  Repeated interruption of large jobs can reduce available memory
  under R. This occurs because memory is allocated dynamically, and
  memory that has been allocated is not freed when you interrupt the
  job (the routine will clean up after itself only if it is allowed to
  complete all computations - when you interrupt you never reach the
  point in the code where the memory is freed). If this becomes an
  issue simply restart R (i.e., exit then run a fresh R session).

\subsection{I have a large number of variables, and when using the
    formula interface I get an error message stating 'invoked with
    improper formula'. I have double checked and everything looks
    fine. Furthermore, it works fine with the data frame interface.}

  The issue is that converting formulas into character strings in
  \texttt{R} appears to be limited to 500 characters. We are not aware
  of a simple workaround so we simply advise that you use the data
  frame interface when this occurs.

\subsection{How can I estimate additive semiparametric models?}

Generalized additive semiparametric models (see Hastie and Tibshirani
(1990) \cite{HASTIE_TIBSHIRANI:1990}) are implemented in the
\texttt{gam} package (though they do not support categorical
variables). The \texttt{gam} package function \texttt{gam()} (the
\texttt{mgcv} package also contains a similar function by the same
name) uses iteratively reweighted least squares and either smoothing
splines (\texttt{s($\cdot$)}) or local polynomial regression fitting
(\texttt{'loess', lo($\cdot$)}, with default manual 'span' of 0.75,
the parameter which controls the degree of smoothing). The following
code snippet demonstrates the capabilities of the \texttt{gam()}
function via the \verb+wage1+ dataset included in the \texttt{np}
packages using three numeric regressors.

\begin{verbatim}
library(gam)
data(wage1)
attach(wage1)
model.gam <- gam(lwage~s(educ)+s(exper)+s(tenure))
par(mfrow=c(2,2))
plot(model.gam,se=T)
detach(wage1)
\end{verbatim}

The \texttt{mgcv} package also has an implementation of generalized
additive models via the identical function name, \texttt{gam()}. The
biggest difference is that this uses generalized cross validation to
select the 'span' (rather than manually) hence the degree of smoothing
becomes part of the method (as is the case for all functions in the
\texttt{np} package). The following code snippet demonstrates the
\texttt{mgcv} implementation of the \texttt{gam()} function.

\begin{verbatim}
library(mgcv)
data(wage1)
attach(wage1)
model.gam <- gam(lwage~s(educ)+s(exper)+s(tenure))
par(mfrow=c(2,2))
plot(model.gam,se=T)
detach(wage1)
\end{verbatim}

  \subsection{I am using \texttt{npRmpi} and am getting an error message
  involving \texttt{dlopen()}}

One of the most common problems experienced by users attempting to
install and run MPI-aware programs is to first correctly identify the
location of libraries and headers for the local MPI installation so
that installation can proceed.

By way of illustration, the following environment variables need to be
set for the MacPorts version of OpenMPI (www.macports.org) running on
Mac OS X 10.8.3 (the environment commands listed below are for those
using the 'bash' shell):

\begin{verbatim}
export LD_LIBRARY_PATH=/opt/local/lib
export RMPI_LIB_PATH=/opt/local/lib
export RMPI_TYPE=OPENMPI
export RMPI_INCLUDE=/opt/local/include/openmpi

launchctl setenv LD_LIBRARY_PATH $LD_LIBRARY_PATH
launchctl setenv RMPI_LIB_PATH $RMPI_LIB_PATH
launchctl setenv RMPI_TYPE $RMPI_TYPE
launchctl setenv RMPI_INCLUDE $RMPI_INCLUDE
\end{verbatim}

Once set, R (and optionally RStudio) ought to function as
expected. However, problems encountered during this phase are best
resolved by someone with familiarity of the local installation.
    
  \subsection{I am using the \texttt{npRmpi} package but when I launch
    one of the demo parallel jobs I get the error \texttt{Error: could
      not find function ``mpi.bcast.cmd''}}

When your demo program stops at the following point in your file
\begin{verbatim}
> mpi.bcast.cmd(np.mpi.initialize(),
+               caller.execute=TRUE)
Error: could not find function "mpi.bcast.cmd"
\end{verbatim}
this likely means that either you have failed to place the
\texttt{.Rprofile} file in the current or root directory as directed,
or the \texttt{.Rprofile} initialization code is not being loaded as
expected.

\begin{enumerate}

\item Make sure a copy of the initialization file \texttt{Rprofile}
  exists in your working or root directory and is named
  \texttt{.Rprofile}

\item Make sure you did not run \texttt{R} with either the
  \texttt{--no-init-file} or \texttt{--vanilla} option (this combines
  a number of options including \texttt{--no-init-file} which will
  disable reading of \texttt{.Rprofile})

\end{enumerate}

\subsection{I have estimated a partially linear model and want to
  extract the gradient/fitted values of the nonparametric component}

People use partially linear models because they focus on the
parametric component and treat the nonparametric component as a
nuisance. In fact, the partially linear model is estimated by
carefully getting rid of the nonparametric component $g(Z)$ prior to
estimation, and then estimating a set of conditional moments
nonparametrically.

However, suppose after getting rid of this nonparametric nuisance
component we then wished to construct a consistent estimator of
$g(Z)$, the nonparametric component for a partially linear model $y =
X\beta + g(Z) + u$. We might proceed as follows.

\begin{verbatim}
library(np)

set.seed(42)

n <- 250
x1 <- rnorm(n)
x2 <- rbinom(n, 1, .5)

z1 <- rbinom(n, 1, .5)
z2 <- rnorm(n)

y <- 1 + x1 + x2 + z1 + sin(z2) + rnorm(n)

## First, construct the partially linear model using local linear 
## regression.

model <- npplreg(y~x1+factor(x2)|factor(z1)+z2,regtype="ll")

## Next, subtract the fitted parametric component from y so that we
## have y-xbetahat. Since we can have factors we need to create the
## 'model matrix' but make sure we don't keep the intercept generated
## by model.matrix hence the [,-1]. This gives us the numeric matrix X
## which we multiply by the coefficient vector to obtain xbetahat which
## we can subtract from y.

y.sub <- y-model.matrix(~x1+factor(x2))[,-1]%*%coef(model)

## Finally, regress this on the nonparametric components Z using npreg.

model.sub <- npreg(y.sub~factor(z1)+z2,regtype="ll",gradients=TRUE)

## Now we can obtain derivatives etc. However, note that this is the
## model containing the transformed y with respect to the nonparametric
## components. We can use gradients(model.sub) etc. or plot them and
## so forth.

plot(model.sub,gradients=TRUE)
\end{verbatim}

\subsection{The R function 'lag()' does not work as I expect it
  to. How can I create the $l$th lag of a numeric variable in R to be
  fed to functions in the \texttt{np} package?}

As of version 0.60-2, time series objects are supported. However, if
you prefer you can use the function \texttt{ts.intersect}, which can
exploit R's lag function but return a suitable data frame, as per the
following illustration:
\begin{verbatim}
data(lynx)
loglynx <- log(lynx)
lynxdata <- ts.intersect(loglynx,
                         loglynxlag1=lag(loglynx,-1),
                         dframe=TRUE)
model <- npregbw(loglynx~loglynxlag1,
                 data=lynxdata)
plot(model)
\end{verbatim}
Note that in order for the above to work, the common argument fed to
\texttt{ts.intersect} must be a \texttt{ts} object, so first cast it
as such if it is not already (\texttt{log(lynx)} is a \texttt{ts}
object since \texttt{lynx} was itself a \texttt{ts} object).

Or, you can use the \texttt{embed} function to accomplish
this task. Here is a simple function that might work more along the
lines that you expect. By default we 'pad' the vector with NAs but you
can switch this to \texttt{FALSE} if you prefer. The function will
return a vector of the same length as the original vector with NA's
padded for the missing values.

\begin{verbatim}
lag.numeric <- function(x,l=1,pad.NA=TRUE) {
  if(!is.numeric(x)) stop("x must be numeric")
  if(l < 1) stop("l (lag) must be a positive integer")
  if(pad.NA) x <- c(rep(NA,l),x)
  return(embed(x,l+1)[,l+1])
}
x <- 1:10
x.lag.1 <- lag.numeric(x,1)
\end{verbatim}

\subsection{Can I provide sample weights to be used by functions in
  the \texttt{np} package?}

Unfortunately, at this stage the answer is 'no', at least not directly
with many of the functions as they stand. However, the function
\texttt{npksum} underlies many of the functions in the \texttt{np}
package and it supports passing of weights, so you may be able to use
this function and do a bit of coding to fulfill your needs. Kindly see
\texttt{?npksum} for illustrations.

Alternatively, if reweighting of sample data is sufficient for your
needs then you can feed the weighted sample realizations directly to
existing functions.

\subsection{Quantile regression is slow, particularly for very
  small/large values of tau. Can this be sped up?}

Yes, indeed this can be the case for extreme values of tau (and not so
extreme values as well). The reason for this is because numerical
methods are used to invert the CDF. This must be done for each
predictor observation requiring the solution to $n$ (or $neval$)
optimization problems. An alternative is to compute the
'pseudo-inverse' via a 'lookup method'. In essence, one computes the
conditional CDF for a range of $y$ values, and then computes the
pseudo-inverse which is defined as
\begin{align*}
  q_{\tau}(x) &= \inf \{ y: \, F(y|x) \geq \tau \}\\
  & = \sup \{ y: \, F(y|x) \le \tau \}
\end{align*}

The following code demonstrates this approach for the example used in
the help file for \texttt{npqreg} (see \texttt{?npqreg}).

\begin{verbatim}
data("Italy")
attach(Italy)
     
bw <- npcdensbw(gdp~year)

## Set a grid of values for which the conditional CDF will be computed
## with a range that extends well beyond the range of the data

n.eval <- 1000
gdp.er <- extendrange(gdp,f=2)
gdp.q <- quantile(gdp,seq(0,1,length=n.eval))
gdp.eval <- sort(c(seq(gdp.er[1],gdp.er[2],length=n.eval),gdp.q))
n.q <- length(gdp.eval)

## We only need to compute the conditional quantiles for each unique
## value of year

year.unique <- unique(year)

## Consider a range of values for tau

tau.seq <- c(0.01,0.05,0.25,0.5,0.75,0.95,0.99)
gdp.tau <- matrix(NA,length(year.unique),length(tau.seq))

for(j in 1:length(tau.seq)) {
  cat("\r",j,"of",length(tau.seq))
  tau <- tau.seq[j]
  for(i in 1:length(year.unique)) {
    F <- fitted(npcdist(bws=c(bw$ybw,bw$xbw),
                        txdat = year,
                        tydat = gdp,
                        exdat = rep(year.unique[i],n.q),
                        eydat = gdp.eval))
    ## For each realization of the predictor, compute the 
    ## the pseudo-inverse
    gdp.tau[i,j] <- ifelse(tau>=0.5, max(gdp.eval[F<=tau]), 
                                     min(gdp.eval[F>=tau]))
  }
}

## Plot the results

plot(year,gdp,ylim=c(min(gdp.tau,gdp),max(gdp.tau,gdp)))     
for(j in 1:length(tau.seq)) {
  lines(year.unique,gdp.tau[,j],col=j+1,lty=j,lwd=2)
}

legend(min(year),max(gdp.tau,gdp),
       paste("tau=",tau.seq),
       col=1:length(tau.seq)+1,
       lty=1:length(tau.seq),
       lwd=2)
\end{verbatim}

\subsection{How can I generate resamples from the unknown distribution
  of a set of data based on my smooth kernel density estimate?}

This can be accomplished by picking a sample realization, uniformly at
random, then drawing from the kernel distribution centered on that
training point with scale equal to the bandwidth. Below is a
demonstration for the 'Old Faithful' data where we draw a random
sample of size $n=1,000$ where a Gaussian kernel was used for the
density estimator.

\begin{verbatim}
data(faithful)
n <- nrow(faithful)

x1 <- faithful$eruptions
x2 <- faithful$waiting

## First compute the bandwidth vector

bw <- npudensbw(~x1+x2,ckertype="gaussian")

## Next generate draws from the kernel density (Gaussian)

n.boot <- 1000

i.boot <- sample(1:n,n.boot,replace=TRUE)
x1.boot <- rnorm(n.boot,x1[i.boot],bw$bw[1])
x2.boot <- rnorm(n.boot,x2[i.boot],bw$bw[2])  

## Plot the density for the bootstrap sample using the original 
## bandwidths
  
plot(npudens(~x1.boot+x2.boot,bws=bw$bw),view="fixed",xtrim=-.2,neval=100)
\end{verbatim}

%% See page 294 and up in cosma_resampling_ch15.pdf in ~/R/

\subsection{Some of my variables are measured with an unusually large
  number of digits\dots should I rescale?}

In general there should be no need to rescale data for one's
statistical analysis. However, occasionally one can encounter issues
with numerical accuracy (e.g.\ numerical 'overflow') regardless of the
method used. It is therefore prudent to be aware of this issue. For
instance, if your dependent variable represents housing prices in a
particular currency and entries are recorded as e.g.\
145,000,000,000,000,000,000 foounits, then it might be prudent to
deflate this variable by $10^{20}$ (i.e.\ 1.45) so that e.g.\ sums of
squares are numerically stable (say when using least squares
cross-validation). Of course you can run your analysis with and
without the adjustment and see whether it matters or not. But it is
sometimes surprising that such things can in fact make a
difference. See \texttt{?scale} for a function whose default method
centers and/or scales the columns of a numeric matrix.

\subsection{The local linear gradient estimates appear to be somewhat
  'off' in that they do not correspond to the first derivative of the
  estimated regression function.}

It is perhaps not a widely known fact that the local linear partial
derivatives obtained from the coefficients of the Taylor
approximation, $\hat b(x)$, are not the analytical derivative of the
estimated regression $\hat g(x)$ with respect to $x$.  The local
linear estimator is obtained by minimizing the following weighted
least squares function (consider the one-predictor case to fix ideas)
\begin{equation*}
\sum_i(Y_i - a - b (x-X_i))^2 K\left(\frac{x-X_i}{h}\right)
\end{equation*}
and the estimated regression function $\hat g(x)$ is given by
\begin{equation*}
\hat g(x) =\hat a 
\end{equation*}
while the gradient is given by
\begin{equation*}
\hat \beta(x)=\hat b.
\end{equation*}
But the analytical gradient (i.e.\ the partial derivative of $\hat
g(x)=\hat a$ with respect to $x$) is \textsl{not} $\hat b$ unless the
bandwidth is very large (i.e.\ $h=\infty$) in which case
$K((x-X_i)/h)=K(0)$ and one gets the standard linear least squares
estimates for $\hat g(x)$ and $\hat\beta(x)$ (if you compute the
partial algebraically you will see they are not the same).

So, the derivative estimates arising directly from the local linear
estimator will differ from the analytical derivatives, even though
they are asymptotically equivalent under standard conditions required
for consistency. Thus, if economic constraints are imposed on the
direct derivatives, this may produce an estimated surface which is not
consistent with the constraints.  This can be avoided by imposing the
constraints on the analytical derivatives of the local polynomial
estimator being used.

\subsection{How can I turn off all console I/O?}

To disable all console I/O, set \texttt{options(np.messages=FALSE)}
and wrap the function call in \texttt{suppressWarnings()} to disable any
warnings printed to the console. For instance
\begin{verbatim}
library(np)
options(np.messages=FALSE)
set.seed(42)
n <- 100
x <- sort(rnorm(n))
z <- factor(rbinom(n,1,.5))
y <- x^3 + rnorm(n)
model.np <- suppressWarnings(npreg(y~x+z))
\end{verbatim}
ought to produce no console I/O whatsoever in the call to
\texttt{npreg}.

\subsection{Is there a way to exploit the sparse nature of the design
  matrix when all predictors are categorical and reduce computation
  time, particularly for cross-validation?}

Certainly. This would occur if, for instance, you had 4 predictors
each of which was binary 0/1, so there are only $2^4=16$ possible
unique rows in the design matrix. The following conducts kernel
regression with exclusively binary predictors by way of illustration.
\begin{verbatim}
## This routine exploits a sparse design matrix when computing the
## kernel estimator of a conditional mean presuming unordered
## categorical predictors. Numerical optimization is undertaken, and
## this function can be much faster than that ignoring the sparse
## structure for large n and small k (the function npreg() currently
## does not attempt to exploit this structure).

rm(list=ls())

## Set the number of observations and number of binary predictors

n <- 1000
k <- 4

## Create data/DGP

z <- matrix(rbinom(n*k,1,.5),n,k)
y <- rowSums(z) + rnorm(n)

## Fire up uniquecombs() on a matrix of discrete support predictors.
## We call the crs() variant of uniquecombs (the function is taken
## from mgcv(), but mgcv() has serious load time overhead, and I don't
## want to rely on other packages unnecessarily).

z.unique <- crs:::uniquecombs(as.matrix(z))
num.z <- ncol(z.unique)
ind <-  attr(z.unique,"index")
ind.vals <-  unique(ind)
c <- nrow(z.unique)
if(c == n) stop("design is not sparse (no repeated rows)")

## Kernel function (li-racine unordered kernel)

kernel <- function(X,x,lambda) ifelse(X==x,1,lambda)

## Least-squares cross-validation objective function

cv.ls.uniquecombs <- function(lambda,y,z,z.unique,ind,ind.vals,num.z,c) {
    g <- numeric()
    for(i in 1:c) {
        zz <- ind == ind.vals[i]
        L <- apply(sapply(1:num.z, function(j){kernel(z[,j],
                                                      z.unique[ind.vals[i],j],
                                                      lambda[j])}),1,prod)
        g[zz] <- (sum(y*L)-(y*L)[zz])/np:::NZD(sum(L)-L[zz])
    }
    return(mean((y-g)^2))
}

## Start timing for comparison with npreg()

ptm <- proc.time()

## Numerical optimization via optim() - could be faster if we also
## used fn.gradient (not done here)

optim.out <- optim(runif(num.z),
                   fn=cv.ls.uniquecombs,
                   method="L-BFGS-B",
                   lower=rep(0,num.z),
                   upper=rep(1,num.z),
                   y=y,
                   z=z,
                   z.unique=z.unique,
                   ind=ind,
                   ind.vals=ind.vals,
                   num.z=num.z,
                   c=c)

## Extract least-squares cross-validation optimal bandwidths

lambda.opt <- optim.out$par

## Compute the estimator using the optimal bandwidths

g <- numeric()
for(i in 1:c) {
    zz <- ind == ind.vals[i]
    L <- apply(sapply(1:num.z, function(j){kernel(z[,j],
                                                  z.unique[ind.vals[i],j],
                                                  lambda.opt[j])}),1,prod)
    g[zz] <- sum(y*L)/np:::NZD(sum(L))
}

## Save execution time for optimization and estimation

t.uniquecombs <- proc.time() - ptm

## Compare timing and results with npreg() (comment out the following
## for general use)

library(np)
g.Formula <- "y ~"
for (p in 1:k) {
  g.Formula <- paste(g.Formula," + factor(z[,",p,"])")
}
g.Formula <- formula(g.Formula)
t.npreg <- system.time(g.npreg <- npreg(g.Formula,
                                        ukertype="liracine",
                                        nmulti=1))

## Compare fitted values for first 10 observations

cbind(g[1:10],fitted(g.npreg)[1:10])

## Compare bandwidths

cbind(lambda.opt,g.npreg$bws$bw)

## Compare objective function values

cbind(optim.out$value,g.npreg$bws$fval)

## Compare computation time in seconds

cbind(t.uniquecombs[1],t.npreg[1])
\end{verbatim}

\subsection{I want to bootstrap the standard errors for the
  coefficients in a varying coefficient specification. Is there a
  simple way to accomplish this?}

The code below presents one way to accomplish this. For this example
the model is
\begin{equation*}
Y_i=\alpha(Z_i)+X_i\beta(Z_i)+\epsilon_i,
\end{equation*}
where $X_i$ is experience and $Z_i$ is tenure. The estimated slope
vector $\beta(Z_i)$ is therefore a function of tenure. We bootstrap
its standard error and then plot the resulting estimate and 95\%
asymptotic confidence bounds.

\begin{verbatim}
library(np)
data(wage1)
## Fit the model
model <- with(wage1,npscoef(tydat=lwage,
                            txdat=exper,
                            tzdat=tenure,
                            betas=TRUE))
beta2 <- coef(model)[,2]
## Bootstrap the standard error for the slope coefficient (there
## will be two coefficient vectors, the intercept and slope 
## for exper, which vary with tenure)
B <- 100
coef.mat <- matrix(NA,nrow(wage1),B)
for(b in 1:B) {
    ## Bootstrap the training data, evaluate on the original
    ## sample realizations, hold the bandwidth constant at
    ## that for the original model/training data
    wage1.boot <- wage1[sample(1:nrow(wage1),replace=TRUE),]
    model.boot <- with(wage1.boot,npscoef(tydat=lwage,
                                          txdat=exper,
                                          tzdat=tenure,
                                          exdat=wage1$exper,
                                          ezdat=wage1$tenure,
                                          betas=TRUE,
                                          bws=model$bw))
    coef.mat[,b] <- coef(model.boot)[,2]
}

se.beta2 <- apply(coef.mat,1,sd)
ci.l <- beta2-1.96*se.beta2
ci.u <- beta2+1.96*se.beta2

ylim <- range(c(beta2,ci.l,ci.u))
with(wage1,plot(tenure,beta2,ylim=ylim))
with(wage1,points(tenure,ci.l,col=2))
with(wage1,points(tenure,ci.u,col=2))
legend("topleft",c("beta2","ci.l","ci.u"),col=c(1,2,2),pch=c(1,1,1),bty="n")
\end{verbatim}

\bibliographystyle{plain} 

\bibliography{np_faq}

\clearpage

\appendix

\section*{Changes from Version 0.60-19 to 0.60-20 [06-Feb-2026]}

\begin{itemize}

\item Fixed np issues 4/6/7/13/18/26/51 and added np.pairs utilities

\item Merged all bug fixes and modifications present in the np package since the previous update of the npRmpi package (0.60-2 [27-Jun-2014]) in to the npRmpi package, updated MPI functionality to reflect those in the most recent Rmpi version (0.7-3.3).

\item Major enhancements to npregiv() and npregivderiv():

\begin{itemize}

  \item Implemented warm-start strategy for improved convergence
  \item Aligned multistart strategy with crsiv/crsivderiv for consistency
  \item Performance optimizations: pre-allocated matrices/lists in iterative loops,
    optimized trapezoidal integration, improved Tikhonov and Ridge calculations
  \item Added S3 methods (print, summary, plot) for better integration with R workflow
  \item Enhanced summaries with bandwidth details and estimation timing information
  \item Alphabetized function arguments for consistency
  \item Fixed initialization of bw.mu.w in npregivderiv
  \item Cleaned up naming convention (phihat to phi throughout)

\end{itemize}

\item Testing improvements:

\begin{itemize}

  \item Added comprehensive unit tests using testthat framework
  \item Expanded test coverage to include distribution, copula, quantile regression,
    tests of independence/specification, and boundary/shape-constrained methods

\end{itemize}

\item Build and maintenance updates:

\begin{itemize}

  \item Refined .Rbuildignore regexes to correctly exclude .git and build artifacts
  \item Added missing imports (graphics, grDevices) to NAMESPACE to resolve global
    function notes
  \item Restored dontrun blocks in documentation to expedite package checks
  \item Suppressed build warnings for non-standard man directory files

\end{itemize}

\item Bug fixes:

\begin{itemize}

  \item Fixed np.plot categorical predictor evaluation
  \item Fixed np package registrations after sync
  \item Synced non-MPI code fixes from npRmpi

\end{itemize}

\end{itemize}

\section*{Changes from Version 0.60-29 to 0.60-20 [11-Feb-2026]}

\begin{itemize}

\item Major enhancements to npregiv() and npregivderiv():

\begin{itemize}
  \item Implemented warm-start strategy for improved convergence
  \item Aligned multistart strategy with crsiv/crsivderiv for consistency
  \item Performance optimizations: pre-allocated matrices/lists in iterative loops,
    optimized trapezoidal integration, improved Tikhonov and Ridge calculations
  \item Added S3 methods (print, summary, plot) for better integration with R workflow
  \item Enhanced summaries with bandwidth details and estimation timing information
  \item Alphabetized function arguments for consistency
  \item Fixed initialization of bw.mu.w in npregivderiv
  \item Cleaned up naming convention (phihat to phi throughout)
\end{itemize}  

\item Testing improvements:

\begin{itemize}
  \item Added comprehensive unit tests using testthat framework
  \item Expanded test coverage to include distribution, copula, quantile regression,
    tests of independence/specification, and boundary/shape-constrained methods
\end{itemize}

\item Build and maintenance updates:

\begin{itemize}
  \item Resolved -Wfree-nonheap-object compiler warnings in nr.c by implementing 
    a safe 0-based allocation strategy for 1-based indexing compatibility
  \item Refined .Rbuildignore regexes to correctly exclude .git and build artifacts
  \item Added missing imports (graphics, grDevices) to NAMESPACE to resolve global
    function notes
  \item Restored \texttt{dontrun} blocks in documentation to expedite package checks
  \item Suppressed build warnings for non-standard man directory files
\end{itemize}  

\item Bug fixes:

\begin{itemize}
  \item Fixed np.plot categorical predictor evaluation
  \item Fixed np package registrations after sync
  \item Synced non-MPI code fixes from npRmpi
\end{itemize}  

\item Documentation updates:

\begin{itemize}
  \item Updated URLs to resolve CRAN check warnings
  \item Updated McMaster website URL to https://experts.mcmaster.ca/people/racinej
  \item Added build notes, worktrees documentation, and CRAN diff summary
  \item Fixed documentation mismatches for npregiv/npregivderiv
\end{itemize}  

\end{itemize}

\section*{Changes from Version 0.60-18 to 0.60-19 [28-Jan-2026]}

\begin{itemize}

\item Added crs to Suggests field in DESCRIPTION per CRAN requirements

\item Utility functions \texttt{integrate.trapezoidal()}, \texttt{NZD()}, \texttt{NZD\_pos()} (new, affect npregiv() and npregivderiv())

\item Miscellaneous typos fixed

\end{itemize}

\section*{Changes from Version 0.60-17 to 0.60-18 [09-Dec-2024]}

\begin{itemize}

\item Patched issue with \texttt{as.double(data)} when data is a NULL object
  reported by Brian Ripley

\item Merged rng pull request \texttt{https://github.com/JeffreyRacine/R-Package-np/pull/48}

\item Incorporated Kurt Hornik's kind suggestion ``If indeed intended as a
  package overview help file, please add \texttt{{\textbackslash}alias\{np-package\}} to file
  \texttt{'np/man/np-package.Rd'}''

\end{itemize}

\section*{Changes from Version 0.60-16 to 0.60-17 [12-Mar-2023]}

\begin{itemize}

\item Fixed warning

\begin{verbatim}
  Check: S3 generic/method consistency Result: WARN
  compute.bootstrap.errors: function(..., bws)
  compute.bootstrap.errors.*} triggered potentially by lack of
  \texttt{...,bw} in functions called
\end{verbatim}

(thanks to Kurt Hornik for assistance!)

\item Updated \texttt{inst/CITATIONS} to get rid of old-style cit and
  bib entries
  
\end{itemize}

\section*{Changes from Version 0.60-15 to 0.60-16 [18-Oct-2022]}

\begin{itemize}

\item Fixed \texttt{warning: a function definition without a prototype is
  deprecated in all versions of C and is not supported in C2x
  [-Wdeprecated-non-prototype]} (thanks Zhenghua!)

\end{itemize}
  
\section*{Changes from Version 0.60-14 to 0.60-15 [09-Oct-2022]}

\begin{itemize}

\item Explicit acknowledgment in \texttt{DESCRIPTION} of code
  \texttt{gsl\_bspline.c/.h} adapted from the GNU GSL library with
  further details appended to \texttt{gsl\_bspline.c/.h} (thanks to
  Professor Brian Ripley for noting this oversight).

\end{itemize}

\section*{Changes from Version 0.60-13 to 0.60-14 [22-Aug-2022]}

\begin{itemize}

\item Added logspline and ks to DESCRIPTION to address NOTE on some system
  builds stating \texttt{Undeclared packages logspline, ks in Rd xrefs}

\item Zhenghua Nie kindly addressed the clang-UBSAN issue in jksum.c
  causing \texttt{runtime error: applying non-zero offset 8 to null pointer}

\end{itemize}

\section*{Changes from Version 0.60-12 to 0.60-13 [15-Aug-2022]}

\begin{itemize}

\item Minor changes to np.Rnw vignette viz Sweave options and class
	(redundancies commented out)

\item Fixed issues relating to new NOTE ``Found if() conditions
  comparing class() to string [..] Use inherits() (or maybe is())
  instead.'' Addressed by using \texttt{isa()}

\end{itemize}

\section*{Changes from Version 0.60-11 to 0.60-12 [12-Aug-2022]}

\begin{itemize}

\item JSS issues corrected in vignette/*.bib and inst/CITATION (use of DOI,
  etc., thanks to Achim Zeileis)

\item Issues with utf8x in entropy\_np.Rnw and np.Rnw corrected (utf8x
  changed to utf8, etc.)

\end{itemize}  

\section*{Changes from Version 0.60-10 to 0.60-11 [04-Jun-2021]}

\begin{itemize}

\item \texttt{npuniden.boundary()} uses empirical support for
  \texttt{a} and \texttt{b} (previously was \texttt{[0,1]}, now
  \texttt{[min(X),max(X)]})

\item Corrected potential issue with \texttt{malloc} failing on null vector
  in C function \texttt{sort\_unique()} detected by development version of
  \texttt{gcc11} (thanks to Professor Brian Ripley for pointing this out
  and for his assistance)

\item Corrected outdated URLs  

\end{itemize}    

\section*{Changes from Version 0.60-9 to 0.60-10 [5-Feb-2020]}

\begin{itemize}

\item Corrected issue \texttt{Documented arguments not in usage in documentation object se: \dots}

\item Removal of directed quotes in some Rd documents, replacement
  with \verb+\sQuote{}+

\item Fixed issue causing rebuilding of vignettes to crash (\texttt{uocquantile()} was the culprit)
  
  
\end{itemize}  

\section*{Changes from Version 0.60-8 to 0.60-9 [24-Oct-2018]}

\begin{itemize}

\item Added support for character expansion to \texttt{npplot()} (which is invoked by calling \texttt{plot()} on an np object) - will take defaults from the environment \texttt{par()} or can be set directly, e.g., \texttt{plot(foo,cex.main=0.8)}

\end{itemize}

\section*{Changes from Version 0.60-7 to 0.60-8 [04-Jun-2018]}

\begin{itemize}

\item Used patch suggested by Scott Thompson for issue https://github.com/JeffreyRacine/R-Package-np/issues/8 regarding \texttt{npcdens()/npcdist()} and formulas

\end{itemize}

\section*{Changes from Version 0.60-6 to 0.60-7 [01-May-2018]}

\begin{itemize}

\item Fix for \texttt{switch()} and zero length character strings that
  affected summary output for certain tests
  
\item Added function for shape constrained bounded univariate PDF and
  CDF estimation (\texttt{npuniden.sc()})

\item Added option for renormalizing improper bounded density
  estimates than can arise from the use of asymmetric negative edge
  kernel functions (\texttt{proper=TRUE},
  \texttt{npuniden.boundary()})

\item Fixed issues with CDF estimation in the presence of large
  bandwidths for bounded density estimates
  (\texttt{npuniden.boundary()})

\end{itemize}

\section*{Changes from Version 0.60-5 to 0.60-6 [12-Jan-2018]}

\begin{itemize}

\item Added more edge kernel functions for
  \texttt{npuniden.boundary()}, some glitches addressed

\item Added asymptotic standard errors and integrated density (CDF) to
  \texttt{npuniden.boundary()} and \texttt{npuniden.reflect()} plus
  additional examples

\item Added least squares cross-validation to
  \texttt{npuniden.boundary()} (default for boundary kernel functions)
  
\end{itemize}

\section*{Changes from Version 0.60-4 to 0.60-5 [04-Jan-2018]}

\begin{itemize}

\item Added two basic functions for univariate bounded kernel density
  estimation, \texttt{npuniden.boundary} and \texttt{npuniden.reflect}

\item More plotting routines accept more passable parameters

\end{itemize}

\section*{Changes from Version 0.60-3 to 0.60-4 [03-Dec-2017]}

\begin{itemize}

\item Default \texttt{plot.errors.style} changed to \texttt{"band"}

\item Using \texttt{wrapLines(strwrap(...))} for summary output for
  model specification test to automatically wrap long formula lines

\item \texttt{plot()} calls \texttt{npplot()} and \texttt{npplot()}
  behaves better when most passable parameters are fed (\texttt{col
    =}, \texttt{lty =}, \texttt{xlab =}, etc.) but there may still be
  room for improvement

\item Added option \texttt{plot.par.mfrow=TRUE/FALSE} to
  \texttt{npplot()} so that the automated setting of
  \texttt{par(mfrow=c(,))} in plot is disabled and the user can do
  this manually if desired

\item Option \texttt{plot.par.mfrow=TRUE/FALSE} can be overridden by
  setting \texttt{options(plot.par.mfrow=TRUE/FALSE)}

\end{itemize}

\section*{Changes from Version 0.60-2 to 0.60-3 [29-Apr-2017]}

\begin{itemize}

\item Fixed the 'cannot find function \texttt{is()}' glitch that just surfaced with R 3.4.0

\item Fixed glitch in \texttt{npconmode()} when randomizing if all probabilities
  are equal

\item Migrated some code from crs (which I wrote) to avoid \texttt{crs:::}

\item Fixed	outstanding glitch in \texttt{npscoef()} with \texttt{tydat}

\item Option \texttt{leave.one.out} not properly implemented in \texttt{npscoef()}, corrected

\item Using pmin/pmax in NZD (parallel min/max more efficient with vectors)

\item Improved screen i/o when \texttt{smooth.residuals=TRUE/FALSE}

\item Corrected glitch in \texttt{npregiv()} where multivariate z would halt with error

\item \texttt{npregiv()} with \texttt{method="Landweber-Fridman"} no longer passes back lists

\item Fixed glitch in \texttt{Kmat.lp} with p=0 and derivatives

\item Tikhonov regularization in \texttt{npregiv()} now supports evaluation data

\item Updated \texttt{npregiv()} (was sorely lacking, did not support eval etc.)

\item Use of \texttt{.onLoad} suggested (by Bernd Bischl)

\item Added \texttt{vignette("entropy\_np",package="np")} to startup message

\item In \texttt{np.distribution.bw.R} default for \texttt{do.full.integral} changed to FALSE

\item Fixed the CDF objective function when averaging over the training data

\item Fixed crash error with \texttt{npcdistbw()} and adaptive bandwidths

\end{itemize}

\section*{Changes from Version 0.60-1 to 0.60-2 [27-Jun-2014]}

\begin{itemize}

\item added timeseries support for all relevant objects (i.e.\ for a
  \texttt{ts()} vector data object \texttt{x},
  \verb^npreg(x~lag(x,-1)+lag(x,-2))^ is now supported)

\item added total time to summary for bandwidth objects

\item \texttt{npqreg()} no longer accepts \texttt{gradients=TRUE} when
  gradients are in fact not supported

\item \texttt{npqreg()} fails with an informative message when passed
  a conditional density bandwidth object

\end{itemize}

\section*{Changes from Version 0.60-0 to 0.60-1 [6-Jun-2014]}

\begin{itemize}

\item Fixed glitch in adaptive\_nn/generalized\_nn bandwidths that
  affected all routines that rely on non-fixed bandwidths

\item Tweaks to search for adaptive\_nn/generalized\_nn initial search values

\item Fixed glitch in local linear estimation with adaptive\_nn bandwidths

\end{itemize}

\section*{Changes from Version 0.50-1 to 0.60-0 [1-Jun-2014]}

\begin{itemize}

\item Ordered kernel types now default to liracine/liracine
  (normalized) for conditional/unconditional objects, respectively
  (the previous default, i.e.\ the Wang van Ryzin kernel, is poorly
  behaved when smoothing out of ordered predictors is appropriate)

\item Added analytical ordered CDF kernels, resulting in significant
  speedups for cross validation with ordered variables

\item Added analytical ordered convolution kernels, resulting in significant
  speedups for least-squares cross validation with ordered variables

\item The entire C backend has been rewritten and improved in almost every
  regard

\item The Rmpi backend has been updated to Rmpi version 0.6-5

\item Glitch in adaptive convolution kernels corrected

\item Added truncated gaussian kernel (see \texttt{ntpgauss()} for
  modifying the truncation radius)

\item Support for trees complete (use \texttt{options(np.tree=TRUE)})
  which when used in conjunction with bounded kernels (i.e.\
  \texttt{"epanechnikov"}/\texttt{"truncated gaussian"}) can reduce
  the computational burden for certain problems

\item Optimizers that make use of Powell's direction set method now accept
  additional arguments that can be used to potentially improve
  default settings

\item Default search settings for optimizers that make use of Powell's
  direction set method should better scale to the range of variables

\item Added mean absolute deviation/1.4826 to mix of robust scale elements

\item Corrected error in order of conditional density/distribution manual
  bandwidths pointed out by Decet Romain

\item Figure in vignette not displaying properly, needed
  \texttt{png=TRUE} reported by Christophe Bontemps

\item Using \texttt{chol2inv}/\texttt{chol} rather than solve
  throughout R routines that rely on inversion

\item Fixed glitch in \texttt{npindexbw()} to stop maxit from blowing
  up every time convergence fails

\item Fixed issue with summary reporting incorrect value of objective function
  in certain bandwidth objects

\item When \texttt{nmulti} $>$ 1, the full multi-starting search
  history is now returned in a vector named fval.history

\item Added \texttt{na.action} for consistency with other R functions
  such as \texttt{lm()}

\item New function \texttt{npquantile()} that returns smooth
  univariate quantiles

\item \texttt{npksum()} explicitly only uses raw bandwidths now (and
  will emit an error if passed numeric scale factors, bandwidth
  objects are still OK)

\item Fixed regression in \texttt{npindex()} with bootstrapped
  standard errors

\item Code makes use of one call to \texttt{npksum()} in
  \texttt{npindex()} and \texttt{npscoef()} where possible rather than
  two separate calls

\item Updated \texttt{npsigtest()} for addition of power and added
  joint test to the mix

\item Changed \texttt{ceiling()} to \texttt{max(1,round())} in
  \texttt{b.star()} per Dimitris Politis's suggestion

\item Reworked the interface for \texttt{npcopula()} to avoid two
  bandwidths and \texttt{density=TRUE} but exploiting passing of
  either \texttt{npudistbw()} (copula) or \texttt{npudensbw} (copula
  density)

\end{itemize}

\section*{Changes from Version 0.40-13 to 0.50-1 [13-Mar-2013]}

\begin{itemize}

\item The functions \texttt{npudist()} and \texttt{npudistbw()} are
  now uncoupled from \texttt{npudens()} and \texttt{npudensbw()}
  (previously they relied on unconditional PDF bandwidths due to the
  lack of a multivariate mixed-data method for selecting bandwidths
  for CDFs - now with Li \& Racine (2013) we have a robust method
  hence the split)

\item The use of \texttt{cdf=TRUE} is deprecated for
  \texttt{npudens()} and \texttt{npudensbw()} objects due to the
  uncoupling described above

\item Fixed glitch in \texttt{gradient} standard errors in
  \texttt{npindex()} where identical standard errors were output in
  \texttt{model\$gerr}

\item Fixed glitch in covariance matrix in \texttt{npindex()}
  (\texttt{"ichimura"}) where covariance matrix was not symmetric

\item Fixed glitch in npksum where use of
  \texttt{bwtype="adaptive\_nn"} and \texttt{operator="integral"}
  produced the survivor function rather than the cumulative
  distribution function

\item Cleaned up internals for \texttt{npcmstest()}

\item Using .onUnload rather than .Last.lib in zzz.R

\item Fixed glitch in \texttt{npreg()} summary where 'Residual
  standard error' was reporting residual variance

\item \texttt{npksum()} functionality extended

\begin{itemize}

\item \texttt{npksum()} can now return the matrix of kernel weights
  (which can be useful for constrained estimation, by way of
  illustration, or constructing novel kernel-based procedures without
  the need to write extensive code)

\item \texttt{npksum()} can now accept different operators on a
  product kernel, for example,
\begin{verbatim}
  npksum(txdat=data.frame(x1,x2),operator=c("derivative","normal"),bws=c(1,1))
\end{verbatim}
  will use the derivative kernel for x1 (i.e. the derivative of the
  gaussian kernel) and the default kernel for x2 (i.e. a standard
  kernel such as the gaussian) thereby allowing the user to program a
  number of estimators such as conditional CDFs etc. that were
  previously not available via \texttt{npksum()}

\end{itemize}

\item Fixed glitch with variable scope where certain objects could not be
  found in the environment

\item Added function \texttt{npcopula()} for d-dimensional copula
  estimation via inversion

\item Modified stopping rules in \texttt{npregiv()} and
  \texttt{npregivderiv()}

\item Added reference to $R^2$ measure (Doksum and Samarov (1995))

\item Startup message points to the faq, faq is now a vignette

\end{itemize}

\section*{Changes from Version 0.40-12 to 0.40-13 [05-Mar-2012]}

\begin{itemize}

\item Added new function \texttt{npregivderiv()} that implements the
  IV derivative method of Florens and Racine (2012)

\item Added more passable parameters to \texttt{npregiv()}
  (multistarting, parameters passed to \texttt{optim()} for
  cross-validation)

\item Changes to code to improve compliance with R 'Writing portable
  packages' guidelines and correct partial argument matches

\end{itemize}

\section*{Changes from Version 0.40-11 to 0.40-12 [24-Nov-2011]}

\begin{itemize}

\item Added option (user request) to hold the bandwidth fixed but
  optimize the parameters in the single index model

\end{itemize}

\section*{Changes from Version 0.40-10 to 0.40-11 [24-Oct-2011]}

\begin{itemize}

\item Corrected code regression in single index errors introduced
  inadvertently in 0.40-10

\end{itemize}

\section*{Changes from Version 0.40-9 to 0.40-10 [24-Oct-2011]}

\begin{itemize}

\item Modified Silverman's adaptive measure of spread to reflect
  changes in \texttt{sd()} (sd on matrix deprecated)

\end{itemize}

\section*{Changes from Version 0.40-8 to 0.40-9 [30-July-2011]}

\begin{itemize}

\item Renamed COPYING file to COPYRIGHTS

\end{itemize}

\section*{Changes from Version 0.40-7 to 0.40-8 [29-July-2011]}

\begin{itemize}

\item Fixed issue where calling \texttt{npplot} resets system seed

\item Updated examples in docs so that plot is recommended throughout
  (and not \texttt{npplot} that is invoked by \texttt{plot})

\item Fixed regression in \texttt{npindex} when \texttt{gradients=TRUE} and
  \texttt{errors=TRUE}

\item Function \texttt{npindex/npindexbw} now accepts additional
  arguments and implements this properly (i.e. proper implementation
  by Tristen of Version 0.30-8/0.30-9 change for \texttt{npindex})

\item Function \texttt{npplreg} now supports factors in the parametric
  part just like \texttt{lm()} does

\end{itemize}

\section*{Changes from Version 0.40-6 to 0.40-7 [8-Jun-2011]}

\begin{itemize}

\item Function \texttt{npregiv} now supports exogenous $X$ and multivariate
  $Z$ and $W$.

\item \texttt{demo(npregiv)} provides a useful illustration.

\end{itemize}

\section*{Changes from Version 0.40-5 to 0.40-6 [1-Jun-2011]}

\begin{itemize}

\item Added a new function \texttt{npregiv} that conducts nonparametric
  instrumental regression a la Darolles, Fan, Florens and Renault
  (2011, Econometrica) and Horowitz (2011, Econometrica). Note that
  this function currently returns the fitted $\varphi(z)$ (i.e.\ lacks
  much functionality relative to other \texttt{np} functions) and is in
  'beta status' until further notice.

\item Added a new dataset \texttt{Engel95} that allows one to estimate
  Engel curves using the new nonparametric instrumental regression
  function \texttt{npregiv}.

\end{itemize}

\section*{Changes from Version 0.40-4 to 0.40-5 [26-Apr-2011]}

\begin{itemize}

\item Fixed issue with \texttt{npindexbw} where, for certain problems,
  starting values needed refinement otherwise convergence would fail
  (we now use an improved normalization for the starting values)

\end{itemize}

\section*{Changes from Version 0.40-3 to 0.40-4 [21-Jan-2011]}

\begin{itemize}

\item Fixed issue with \texttt{ckertype} and \texttt{ckerorder} not
  being propagated in \texttt{np.singleindex.bw.R}

\item Fixed issue with negative penalties being returned by
  \texttt{bwmethod="cv.aic"} in \texttt{npregbw} (ought to have been
  +infinity)

\item Error being thrown by \texttt{system(..., intern=TRUE)} when
  \texttt{mpi.quit()} is called, changed to FALSE (change to
  \texttt{system()} behaviour detailed in R CHANGELOG 2.12.0)

\end{itemize}

\section*{Changes from Version 0.40-1 to 0.40-3 [23-Jul-2010]}

\begin{itemize}

\item Added random seed (defaults to 42) to \texttt{npscoefbw} to ensure
  consistent values for optimization for successive invocations on the
  same data

\item Fixed glitch in multistarting in \texttt{npscoefbw} whereby
  multistarting was not working (always returned last computed
  function value and not the minimum)

\item Fixed issue for \texttt{npRmpi} where the \texttt{C} code
  underlying regression cross-validation (code in \texttt{jksum.c})
  differs between np and npRmpi (both are correct with the latter
  being a tad slower)

\item Fixed a scope issue whereby a user would write a function that
  calls an \texttt{np/npRmpi} command, however, objects passed to the
  user's function and called by the \texttt{np/npRmpi} command
  (i.e. such as \texttt{newdata}) cannot be found in the environment
  yet they exist outside of the function

\item Fixed issue with \texttt{bwscaling=TRUE} and
  \texttt{bwmethod="cv.aic"} in npreg

\end{itemize}

\section*{Changes from Version 0.40-0 to 0.40-1 [4-Jun-2010]}

\begin{itemize}

\item Added asymptotic standard errors to \texttt{npindex} for the
  Klein and Spady and Ichimura parameter estimates which, when
  \texttt{gradients=TRUE}, can be extracted via \texttt{vcov(foo)}
  where \texttt{foo} is a npsingleindex object (the Z-scores can be
  obtained via \texttt{Z <- coef(foo)[-1]/sqrt(diag(vcov(foo)))[-1]})

\end{itemize}

\section*{Changes from Version 0.30-9 to 0.40-0 [25-May-2010]}

\begin{itemize}

\item Modified codebase to enable dynamic spawning for
  interactive sessions in \texttt{npRmpi}

\item Interactive examples supported in \texttt{npRmpi}

\end{itemize}

\section*{Changes from Version 0.30-8 to 0.30-9 [17-May-2010]}

\begin{itemize}

\item Fixed issue where \texttt{ukertype} and \texttt{okertype} were being
  ignored by \texttt{npscoef}

\item Fixed code regression (dating to version 0.30-4) where
  \texttt{random.seed=42} was not initialized in functions
  \texttt{npcmstest}, \texttt{npdeneqtest}, \texttt{npindexbw},
  \texttt{npsdeptest}, \texttt{npqcmstest}, \texttt{npsigtest},
  \texttt{npsymtest}, \texttt{npunitest}, and \texttt{npplot}

\item Fixed issue with saving and restoring random seed in \texttt{npdeptest}

\item Changes to codebase to modify method used to prevent division by
  zero

\item New vignette for the \texttt{npRmpi} package
  \texttt{(vignette("npRmpi",package="npRmpi"))}


\end{itemize}

\section*{Changes from Version 0.30-7 to 0.30-8 [20-Apr-2010]}

\begin{itemize}

\item Implemented moment version of metric entropy in \texttt{npsymtest}
  and \texttt{npunitest} with warnings about their use documented
  carefully and exceptions trapped and warnings issuing when detected
 
\item Cleaned up print/summary output formatting of some functions

\end{itemize}

\section*{Changes from Version 0.30-6 to 0.30-7 [15-Feb-2010]}

\begin{itemize}

\item Added function \texttt{npunitest} for entropy-based testing of
  equality of univariate densities as described in Maasoumi and Racine
  (2002)

\item Updated vignette to reflect new functions from 0.30-4 upwards
  (Table 1: np functions)

\end{itemize}

\section*{Changes from Version 0.30-5 to 0.30-6 [3-Feb-2010]}

\begin{itemize}

\item Added function \texttt{npsdeptest} for entropy-based testing of
  nonlinear serial dependence described in Granger, Maasoumi and
  Racine (2004)

\item Added function \texttt{npdeptest} for entropy-based testing of
  nonlinear pairwise dependence described in Maasoumi and Racine
  (2002)

\item Added more bootstrap options to \texttt{npsymtest} (now both iid
  and time-series bootstrapping are supported)

\item Cleaned up summary formatting in the vignette by adding
  \verb+\usepackage[utf8x]{inputenc}+ to the Sweave file np.Rnw

\item Fixed issue with saving and restoring random seed when there was
  none in the environment
  
\end{itemize}

\section*{Changes from Version 0.30-4 to 0.30-5 [29-Jan-2010]}

\begin{itemize}

\item Added function \texttt{npdeneqtest} for integrated squared
  difference testing of equality of densities as described in
  Maasoumi, Li, and Racine (2009), Journal of Econometrics

\item Save random seed prior to setting seed in certain functions,
  then restore seed after function completes

\end{itemize}

\section*{Changes from Version 0.30-3 to 0.30-4 [27-Jan-2010]}

\begin{itemize}

\item Added function \texttt{npsymtest} for entropy-based testing of
  symmetry described in Maasoumi and Racine (2009), Econometric
  Reviews

\item Added function \texttt{b.star} that automates block length
  selection for the stationary and circular bootstrap

\item Cleaned up docs

\end{itemize}

\section*{Changes from Version 0.30-2 to 0.30-3 [28-May-2009]}

\begin{itemize}

\item Corrected error in Epanechnikov convolution kernels for fixed
  and generalized bandwidth objects

\item Changed default example in \texttt{npscoef}

\end{itemize}

\section*{Changes from Version 0.30-1 to 0.30-2 [19-Apr-2009]}

\begin{itemize}

\item \texttt{min(std,IQR/1.348)} is the adaptive measure of spread. We
  now test for the pathological case where \texttt{IQR=0} but \texttt{std>0}
  and return \texttt{std} in this instance

\end{itemize}

\section*{Changes from Version 0.30-0 to 0.30-1 [29-Jan-2009]}

\begin{itemize}

\item \texttt{predict()} now supports bandwidth, density, distribution,
  conbandwidth, condensity, and condistribution objects

\item Consistently allow predictions for categorical values outside of
  support of training data

  Note that predictions based upon unconditional density objects
  defined over categorical variables that lie outside the support of
  the training data may no longer be true probabilities (i.e., as
  defined over the training data and the extended/augmented support --
  their sum may exceed one) and may therefore require renormalization
  by the user

\item Fixed a numerical issue which could hinder \texttt{npregbw()}'s
  cross validation with higher-order kernels

\item Default \texttt{nmulti} in \texttt{npplregbw()} is now set correctly

\item Fixed a bug with the ridging routine in \texttt{npscoefbw()}, added
  ridging to \texttt{npscoef()}

\item Fixed minor i/o issue with \texttt{Multistart 1 of...} using
  \texttt{npscoefbw()}

\end{itemize}

\section*{Changes from Version 0.20-4 to 0.30-0 [15-Jan-2009]}

\begin{itemize}

\item Added basic user-interrupt checking for all underlying C code so
  that either \verb+<Ctrl-C>+ (Rterm) or the 'STOP' icon (Rgui) will
  interrupt all running processes. This has a number of desirable side
  effects in addition to being able to interrupt C-based processes
  including i) R no longer showing up as 'not responding' under the
  task manager (Windows) or the activity monitor (Mac OS X) and ii)
  buffered output now being correctly displayed when using Rgui under
  Windows and Mac OS X

  Note that repeated interruption of large jobs can reduce available
  memory under R - if this becomes an issue (i.e., you get a 'cannot
  allocate...' error under R) simply restart R (i.e., exit then run a
  fresh R session)

\item Added a function \texttt{npseed()} that allows the user to
  set/reset the random seed for all underlying C routines

\item Fixed a bug that caused \texttt{npplregbw()} to ignore any
  kernel options for the regression of $y$ on $z$

\item Refined certain constants used in the normal-reference density
  bandwidth rule for increased accuracy

\item Moved from using the maximum likelihood estimate of variance
  throughout to the degrees of freedom corrected estimate (all
  variance estimates now change by the factor (n-1)/n)

\end{itemize}

\section*{Changes from Version 0.20-3 to 0.20-4 [19-Nov-2008]}

\begin{itemize}

\item Using an adaptive measure of spread throughout.  The scale
  factor reported for a bandwidth can appear to be small when the
  sample standard deviation of the associated variable is inflated due
  to the presence of outliers.  Furthermore, supplying a scale factor
  of, say, 1.06 for density estimation when there are outliers that
  inflate the standard deviation may oversmooth rather dramatically in
  the presence of outliers.  We now use the measure found in Silverman
  (1986, equation (3.30)) which is min(standard deviation,
  interquartile range/1.349). This robust choice produces expected
  results for scale factors in the presence of outliers

\end{itemize}

\section*{Changes from Version 0.20-2 to 0.20-3[14-Nov-2008] }

\begin{itemize}

\item Fixed a typo which caused \texttt{predict()} and \texttt{plot()} to
  abort when called on \texttt{plregression} objects, and which also
  prevented \texttt{print()} and \texttt{summary()} from printing
  information about the kernels used when called on \texttt{plregression}
  objects

\item Fixed a typo which caused partially linear regressions to crash
  when out-of-sample responses were provided with evaluation data

\end{itemize}

\section*{Changes from Version 0.20-1 to 0.20-2 [02-Nov-2008]}

\begin{itemize}

\item Allow for evaluation outside of discrete support of factors in
  \texttt{npksum()} and fixed a warning in jksum

\item Fixed a bug which lead to unpredictable behavior when there were
  more categorical values for the training data than realisations

\end{itemize}

\section*{Changes from Version 0.20-0 to 0.20-1 [13-Aug-2008]}

\begin{itemize}

\item Work-around for scale-factor issues during \texttt{npregbw()} cv
  when changing the training data

\end{itemize}

\section*{Changes from Version 0.14-3 to 0.20-0 [28-Jul-2008]}

\begin{itemize}

\item \texttt{npksum()} now supports an expanded set of kernels
  (including convolution, derivative and integral), which can be
  selected via the \texttt{operator =} argument

\item Automatic bandwidth searches are now performed when attempting
  to evaluate on data without bandwidths. This allows users to combine
  bandwidth selection and estimation in one step

\item The \texttt{npsigtest()} interface is brought in line with other
  functions (S3)

\item Significance tests can now be performed on \texttt{npreg()}
  outputs, so \texttt{npsigtest(modelname)} is now supported

\item Added a vignette and faq. To see the vignette try
  \texttt{vignette("np",package="np")}

\item \texttt{summary()} on \texttt{npconmode()} now properly
  retrieves names from bandwidth objects

\item Fixed the 6th and 8th order epanechnikov kernels

\item Fixed some quietness issues

\item \texttt{npplot()} now returns data upon request for conditional
  densities

\item \texttt{npreg()} and \texttt{npcdens()} now take the appropriate
  limits in some pathological cases

\item User supplied bandwidths now operate seamlessly with the formula
  interface

\end{itemize}

\section*{Changes from Version 0.14-2 to 0.14-3 [02-May-2008]}

\begin{itemize}

\item Fixed a glitch that only arose when using the \texttt{liracine}
  unordered kernel in the presence of irrelevant variables. The upper
  bound for numerical search was constrained to be (c-1)/c [that for
  the \texttt{aitchisonaitken} unordered kernel] but ought to have been
  1. The summary output would therefore show a value of lambda hitting
  the (smaller) upper bound (c-1)/1 when it may have hit the (larger)
  upper bound 1

\end{itemize}

\section*{Changes from Version 0.14-1 to 0.14-2 [11-Jan-2008]}

\begin{itemize}

\item Relaxed checking tolerances slightly to prevent spurious
  'invalid bandwidth' errors

\item Empty sections were removed from help files

\item \texttt{example(foobar)} now works again. This was disabled in
  0.14-1 at the request of the \texttt{R} maintainers in order to shorten
  the duration of \texttt{R CMD check}. All examples remained in the help
  files but due to the presence of 'dontrun' they were not run when
  \texttt{example(foobar)} is requested. Now a limited subset is run
  while the full set of examples remain in the documents

\end{itemize}

\section*{Changes from Version 0.13-1 to 0.14-1 [18-Dec-2007] }

\begin{itemize}

\item Now use \texttt{optim()} for minimisation in single index and
  smooth coefficient models

\item Fixed bug in klein-spady objective function

\item Standard errors are now available in the case of no continuous
  variables

\item Summary should look prettier, print additional information

\item Tidied up lingering issues with out-of-sample data and
  conditional modes

\item Fixed error when plotting asymptotic errors with conditional
  densities

\item Fixed a bug in \texttt{npplot()} with partially linear regressions
  and \texttt{plot.behavior="data"} or \texttt{"plot-data"}

\item Maximum default number of multistarts is 5

\item Least-squares cross-validation of conditional densities uses a
  new, much faster algorithm

\item New, faster algorithm for least-squares cross-validation for
  both local-constant and local linear regressions

  Note that the estimator has changed somewhat: both cross-validation
  and the estimator itself use a method of shrinking towards the local
  constant estimator when singularity would otherwise lead to the
  breakdown of the estimator. This arises in sparse data settings in
  conjunction with small bandwidths for one or more regressor

\item Optimised smooth coefficient code, added ridging

\item Fixed bug in uniform CDF kernel

\item Fixed bug where \texttt{npindexbw()} would ignore
  \texttt{bandwidth.compute = FALSE} and compute bandwidths when
  supplied with a preexisting bw object

\item Now can handle estimation out of discrete support

\item Summary would misreport the values of discrete scale factors
  which were computed with \texttt{bwscaling = TRUE}

\end{itemize}

\section*{Changes from Version 0.12-1 to 0.13-1  [03-May-2007]}

\begin{itemize}

\item Bandwidths are now checked for validity based on their variable
  and kernel types

\item np now does a better job of preserving names of some 'y' data

\item Names of coefficients returned from \texttt{coef()} now match
  variable names

\item Fixed some corner cases in \texttt{npksum()} involving the
  dimensionality of outputs

\item Fixed deprecation warnings in \texttt{R} 2.5.0 caused by use of \$
  on atomic objects

\item Various and sundry bug fixes in \texttt{npscoef()}

\item \texttt{npscoef()} now handles discrete 'z' data

\item Predict now accepts the argument 'se.fit', like predict.lm

\item Fixed bug where incorrect asymptotic standard errors of
  gradients for regression objects were being displayed in \texttt{npplot()}

\item Fixed bug where errors of gradients of regression objects were
  not being returned in matrix form

\item \texttt{vcov()} now works with partially linear regression objects

\item Fixed detection of evaluation responses when using the formula
  interface

\item Pre-computed bandwidth objects are now provided for some of the
  more computationally burdensome examples

\item Added Jeffrey Wooldridge's WAGE1 dataset with qualitative
  variables (married, female, nonwhite)

\item Predictions outside of discrete support for regressions and
  conditional densities are now allowed

\item Fixed sign issue with scaling of standard errors in the single
  index model

\item Fixed error when calculating some bandwidths/scale factors for
  display purposes

\item Bug in passing certain arguments to \texttt{npcdensbw()} fixed

\item Added predict method for qregression objects

\item Proper normalisation for liracine kernel shown in summary

\item Fixed output bug ($\hat ~$H) in summary method for sigtest
  objects

\item Fixed regression with plotting of bootstrapped errors in
  perspective plots

\item \texttt{npcdist()} no longer incorrectly calls \texttt{npcdens()}

\item Fixed spacing between var name and p-value in significance test
  summaries

\end{itemize}

\section*{Version 0.12-1 [19-Nov-2006]}

\begin{itemize}

\item Initial release of the np package on CRAN

\end{itemize}


\end{document}
