https://github.com/cran/spatstat
Tip revision: 23d61251adb9bd109605170b55856851ca066bbc authored by Adrian Baddeley on 08 May 2017, 13:31:46 UTC
version 1.51-0
version 1.51-0
Tip revision: 23d6125
dimhat.Rd
\name{dimhat}
\alias{dimhat}
\title{
Estimate Dimension of Central Subspace
}
\description{
Given the kernel matrix that characterises a central subspace,
this function estimates the dimension of the subspace.
}
\usage{
dimhat(M)
}
\arguments{
\item{M}{
Kernel of subspace. A symmetric, non-negative definite, numeric
matrix, typically obtained from \code{\link{sdr}}.
}
}
\details{
This function computes the maximum descent estimate of
the dimension of the central subspace with a given kernel matrix \code{M}.
The matrix \code{M} should be the kernel matrix of a central subspace,
which can be obtained from \code{\link{sdr}}. It must be a symmetric,
non-negative-definite, numeric matrix.
The algorithm finds the eigenvalues
\eqn{\lambda_1 \ge \ldots \ge \lambda_n}{lambda[1] \ge ...\ge lambda[n]}
of \eqn{M},
and then determines the index \eqn{k} for which
\eqn{\lambda_k/\lambda_{k-1}}{lambda[k]/lambda[k-1]} is greatest.
}
\value{
A single integer giving the estimated dimension.
}
\seealso{
\code{\link{sdr}}, \code{\link{subspaceDistance}}
}
\references{
Guan, Y. and Wang, H. (2010)
Sufficient dimension reduction for spatial point
processes directed by Gaussian random fields.
\emph{Journal of the Royal Statistical Society, Series B},
\bold{72}, 367--387.
}
\author{
Matlab original by Yongtao Guan,
translated to \R by Suman Rakshit.
}
\keyword{array}
\keyword{algebra}
\keyword{multivariate}