%\VignetteIndexEntry{Package Frontiles}
%\VignetteDepends{}
%\VignetteKeywords{multivariate}
%\VignettePackage{fontiles}
\documentclass[a4paper]{article}
\usepackage{Sweave}
\usepackage{times}
\usepackage{mathptm}
\usepackage{hyperref}
\usepackage{natbib}

\renewcommand{\thefootnote}{\fnsymbol{footnote}}
\newcommand{\strong}[1]{{\normalfont\fontseries{b}\selectfont #1}}
\let\pkg=\strong
\RequirePackage{alltt}
\newenvironment{example}{\begin{alltt}}{\end{alltt}}
\newenvironment{smallexample}{\begin{alltt}\small}{\end{alltt}}
\newcommand{\code}[1]{\texttt{\small #1}}
\def\RR{\textsf{R}\/}


\title{Package Frontiles}
\author{Abdelaati Daouia\footnote{daouia@cict.fr}, Thibault Laurent\footnote{thibault.laurent@univ-tlse1.fr} \cr
{\normalsize Toulouse School of Economics}}
\begin{document}
\maketitle

<<echo=FALSE>>=
owidth <- getOption("width")
options("width"=70)
ow <- getOption("warn")
options("warn"=-1)
.PngNo <- 0
@


<<label=bfig,echo=FALSE,eval=FALSE>>=
.PngNo <- .PngNo + 1; file <- paste("Fig-bitmap-", .PngNo, ".pdf", sep="")
pdf(file=file, width = 7, height = 7, pointsize = 18, bg = "white")
@

<<label=bfig2,echo=FALSE,eval=FALSE>>=
.PngNo <- .PngNo + 1; file <- paste("Fig-bitmap-", .PngNo, ".pdf", sep="")
pdf(file=file, width = 7, height = 7, pointsize = 14, bg = "white")
@

<<label=zfig,echo=FALSE,eval=FALSE>>=
dev.null <- dev.off()
cat("\\includegraphics[width=0.65\\textwidth]{", file, "}\n\n", sep="")
@

<<label=zfig2,echo=FALSE,eval=FALSE>>=
dev.null <- dev.off()
cat("\\includegraphics[width=0.65\\textwidth]{", file, "}\n\n", sep="")
@

For our illustrations, we consider a univariate data set with one input and one output, reported
by Cazals, Florens and Simar (2002) on the delivery activity of the postal services in France. 
The original data set contains information about 9521 post offices $(X_i,Y_i)$ oberved 
in 1994, with $X_i$ being the labor cost (measured by the quantity of labor which represents
more than $80\%$ of the total cost of the delivery activity) and the output $Y_i$ is defined 
as the volume of delivered mail (in number of objects). Here, we restrict our illustration to 
the $n_1=4000$ sample points with the smallest inputs $X_i$.
<<>>=
library(frontiles)
data(burposte)
smallest<-sort(burposte$xinput,index.return=TRUE)$ix[1:4000]
sample.burposte<-burposte[1:9521%in%smallest,]
@
We represent here the scatter plot of the sample firms, where \code{xtab} is
the vector of input and \code{ytab} the vector of output: 

<<label=plot1,fig=FALSE,echo=FALSE,eval=FALSE>>=
xtab<-sample.burposte$xinput
ytab<-sample.burposte$yprod
plot(ytab~xtab, pch=16,col='blue2')
@

\begin{figure}[htbp]
\begin{center}
<<results=tex,echo=FALSE>>=
<<bfig>>
<<plot1>>
<<zfig>>
@
\end{center}
\caption{Representation of the sample points}
\end{figure}



\section*{References}

\begin{description}
\bibitem[\protect\citeauthoryear{Daouia and Simar}{Daouia and Simar}{2007}]{daouia:2007}
Daouia, A., Simar, L. 2007.
\newblock {Nonparametric efficiency analysis: A multivariate conditional quantile approach}.
\newblock {Journal of Econometrics 140}
\newblock 375-400.
\end{description}

\end{document}