\name{LinStatExpCov}
\alias{LinStatExpCov}
\alias{lmult}
\title{
Linear Statistics with Expectation and Covariance
}
\description{
Strasser-Weber type linear statistics and their expectation
and covariance under the independence hypothesis
}
\usage{
LinStatExpCov(X, Y, ix = NULL, iy = NULL, weights = integer(0),
subset = integer(0), block = integer(0), checkNAs = TRUE,
varonly = FALSE, nresample = 0, standardise = FALSE,
tol = sqrt(.Machine$double.eps))
lmult(x, object)
}
\arguments{
\item{X}{numeric matrix of transformations.}
\item{Y}{numeric matrix of influence functions.}
\item{ix}{an optional integer vector expanding \code{X}.}
\item{iy}{an optional integer vector expanding \code{Y}.}
\item{weights}{an optional integer vector of non-negative case weights.}
\item{subset}{an optional integer vector defining a subset of observations.}
\item{block}{an optional factor defining independent blocks of observations.}
\item{checkNAs}{a logical for switching off missing value checks. This
included switching off checks for suitable values of \code{subset}.
Use at your own risk.}
\item{varonly}{a logical asking for variances only.}
\item{nresample}{an integer defining the number of permuted statistics to draw.}
\item{standardise}{a logical asking to standardise the permuted statistics.}
\item{tol}{tolerance for zero variances.}
\item{x}{a contrast matrix to be left-multiplied in case \code{X} was a factor.}
\item{object}{an object of class \code{LinStatExpCov}.}
}
\details{
The function, after minimal preprocessing, calls the underlying C code
and computes the linear statistic, its expectation and covariance and,
optionally, \code{nresample} samples from its permutation distribution.
When both \code{ix} and \code{iy} are missing, the number of rows of
\code{X} and \code{Y} is the same, ie the number of observations.
When \code{X} is missing and \code{ix} a factor, the code proceeds as
if \code{X} were a dummy matrix of \code{ix} without explicitly
computing this matrix.
Both \code{ix} and \code{iy} being present means the code treats them
as subsetting vectors for \code{X} and \code{Y}. Note that \code{ix = 0}
or \code{iy = 0} means that the corresponding observation is missing
and the first row or \code{X} and \code{Y} must be zero.
\code{lmult} allows left-multiplication of a contrast matrix when \code{X}
was (equivalent to) a factor.
}
\value{
A list.
}
\references{
Strasser, H. and Weber, C. (1999). On the asymptotic theory of permutation
statistics. \emph{Mathematical Methods of Statistics} \bold{8}(2), 220--250.
}
\examples{
wilcox.test(Ozone ~ Month, data = airquality, subset = Month \%in\% c(5, 8))
aq <- subset(airquality, Month \%in\% c(5, 8))
X <- as.double(aq$Month == 5)
Y <- as.double(rank(aq$Ozone))
doTest(LinStatExpCov(X, Y))
}
\keyword{htest}