Revision d55e8b38f04442926fbd3c06051c3552f82ea9c8 authored by Roger Koenker on 03 June 2019, 11:40:03 UTC, committed by cran-robot on 03 June 2019, 11:40:03 UTC
1 parent b9eecff
critval.Rd
\name{critval}
\alias{critval}
\title{
Hotelling Critical Values
}
\description{
Critical values for uniform confidence bands for rqss fitting
}
\usage{
critval(kappa, alpha = 0.05, rdf = 0)
}
\arguments{
\item{kappa}{
length of the tube
}
\item{alpha}{
desired non-coverage of the band, intended coverage is 1 - alpha
}
\item{rdf}{
"residual" degrees of freedom of the fitted object. If \code{rdf=0}
then the Gaussian version of the critical value is computed, otherwise
the value is based on standard Student t theory.
}
}
\value{
A scalar critical value that acts as a multiplier for the uniform
confidence band construction.
}
\details{
The Hotelling tube approach to inference has a long and illustrious
history. See Johansen and Johnstone (1989) for an overview. The implementation
here is based on Sun and Loader (1994) and Loader's \pkg{locfit} package, although
a simpler root finding approach is substituted for the iterative method used
there. At this stage, only univariate bands may be constructed.
}
\references{
Hotelling, H. (1939): ``Tubes and Spheres in $n$-spaces, and a class
of statistical problems,'' \emph{Am J. Math}, 61, 440--460.
Johansen, S., I.M. Johnstone (1990): ``Hotelling's
Theorem on the Volume of Tubes: Some Illustrations in Simultaneous
Inference and Data Analysis,'' \emph{The Annals of Statistics}, 18, 652--684.
Sun, J. and C.V. Loader: (1994) ``Simultaneous Confidence Bands for Linear Regression
and smoothing,'' \emph{The Annals of Statistics}, 22, 1328--1345.
}
\seealso{
\code{\link{plot.rqss}}
}
\keyword{regression}
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