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\name{covComed}
\title{Co-Median Location and Scatter "Covariance" Estimator}
\alias{covComed}
%%TODO: these two are not yet imported and hence not yet documented below:
\alias{comedian}
\alias{COM}
\alias{.wgtFUN.covComed}
%
\concept{Co-median}
\concept{Comedian}
\description{
Compute (versions of) the (multivariate) \dQuote{Comedian} covariance,
i.e., multivariate location and scatter estimator
}
\usage{
covComed(X, n.iter = 2, reweight = FALSE, tolSolve = control$tolSolve,
trace = control$trace, wgtFUN = control$wgtFUN,
control = rrcov.control())
% comedian(...)
% COM(...)
}
\arguments{
\item{X}{data matrix of dimension, say \eqn{n \times p}{n x p}.}
\item{n.iter}{number of comedian() iterations. Can be as low as zero.}
\item{reweight}{logical indicating if the final distances and weights
should be recomputed from the final \code{cov} and \code{center}.
The default is currently \code{FALSE} because that was implicit in
the first version of the \R code.}
\item{tolSolve}{a numerical tolerance passed to \code{\link{solve}}.}
\item{trace}{logical (or integer) indicating if intermediate results
should be printed; defaults to \code{FALSE}; values \eqn{\ge 2}{>= 2}
also produce print from the internal (Fortran) code.}
\item{wgtFUN}{a character string or \code{\link{function}}, specifying
how the weights for the reweighting step should be computed. The default,
\code{wgtFUN = "01.original"} corresponds to 0-1 weights as proposed
originally. Other predefined string options are available, though
experimental, see the experimental \code{.wgtFUN.covComed} object.}
\item{control}{a list with estimation options - this includes those
above provided in the function specification, see
\code{\link{rrcov.control}} for the defaults. If \code{control} is
supplied, the parameters from it will be used. If parameters are
passed also in the invocation statement, they will override the
corresponding elements of the control object.}
}
\details{
.. not yet ..
}
\value{
an object of class \code{"covComed"} which is basically a list with components
\item{comp1 }{Description of 'comp1'}
\item{comp2 }{Description of 'comp2'}
... FIXME ...
}
\references{
Falk, M. (1997)
On mad and comedians.
\emph{Annals of the Institute of Statistical Mathematics} \bold{49}, 615--644.
Falk, M. (1998).
A note on the comedian for elliptical distributions.
\emph{Journal of Multivariate Analysis} \bold{67}, 306--317.
}
\author{
Maria Anna di Palma (initial), Valentin Todorov and Martin Maechler
}
\seealso{
\code{\link{covMcd}}, etc
}
\examples{
data(hbk)
hbk.x <- data.matrix(hbk[, 1:3])
(cc1 <- covComed(hbk.x))
(ccW <- covComed(hbk.x, reweight=TRUE))
cc0 <- covComed(hbk.x, n.iter=0)
cc0W <- covComed(hbk.x, n.iter=0, reweight=TRUE)
stopifnot(all.equal(unclass(cc0), # here, the 0-1 weights don't change:
cc0W[names(cc0)], tol=1e-12, check.environment = FALSE),
which(cc1$weights == 0) == 1:14,
which(ccW$weights == 0) == 1:14,
which(cc0$weights == 0) == 1:14)
%% TODO : more
## Martin's smooth reweighting:
## List of experimental pre-specified wgtFUN() creators:
## Cutoffs may depend on (n, p, control$beta) :
str(.wgtFUN.covComed)
}
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