% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/smsncut.R
\name{cutoff_variance}
\alias{cutoff_variance}
\title{Asymptotic variance of the plug-in cutoff estimator}
\usage{
cutoff_variance(
  c_star,
  theta0,
  theta1,
  family0,
  family1,
  lambda0,
  lambda1,
  pi0,
  pi1,
  hess0,
  hess1,
  n0,
  n1,
  ridge = 1e-06
)
}
\arguments{
\item{c_star}{Numeric. The plug-in optimal cutoff.}

\item{theta0}{Numeric vector. MLE for group 0.}

\item{theta1}{Numeric vector. MLE for group 1.}

\item{family0}{Character. Family for group 0.}

\item{family1}{Character. Family for group 1.}

\item{lambda0}{Positive numeric. Cost of a false positive.}

\item{lambda1}{Positive numeric. Cost of a false negative.}

\item{pi0}{Numeric in \eqn{(0,1)}. Prevalence of non-diseased.}

\item{pi1}{Numeric in \eqn{(0,1)}. Prevalence of diseased.}

\item{hess0}{Numeric matrix. Hessian of the negative log-likelihood for
group 0 at the MLE (from \code{\link{smsn_fit}}).}

\item{hess1}{Numeric matrix. Hessian for group 1.}

\item{n0}{Integer. Group-0 sample size.}

\item{n1}{Integer. Group-1 sample size.}

\item{ridge}{Numeric. Ridge added to each Hessian diagonal for numerical
stability. Default \code{1e-6}.}
}
\value{
Numeric scalar. The asymptotic variance \eqn{V}.
}
\description{
Computes the closed-form plug-in asymptotic variance of \eqn{\hat{c}}
under separate SMSN maximum-likelihood fits (Theorem 5.13 and
Proposition 5.15 of de Paula et al., 2026):
\deqn{V = \frac{[\nabla_\theta\varphi]^\top \Sigma_{\mathrm{sep}}
  [\nabla_\theta\varphi]}{[\partial_c\varphi]^2},}
where \eqn{\Sigma_{\mathrm{sep}} = n \cdot
\mathrm{blockdiag}(H_0^{-1}, H_1^{-1})} and \eqn{H_k} is the Hessian
of the negative log-likelihood for group \eqn{k} (equation (26)).
}
