\HeaderA{cov.trob}{Covariance Estimation for Multivariate t Distribution}{cov.trob}
\keyword{multivariate}{cov.trob}
\begin{Description}\relax
Estimates a covariance or correlation matrix assuming the data came
from a multivariate t distribution: this provides some degree of
robustness to outlier without giving a high breakdown point.
\end{Description}
\begin{Usage}
\begin{verbatim}
cov.trob(x, wt = rep(1, n), cor = FALSE, center = TRUE, nu = 5,
         maxit = 25, tol = 0.01)
\end{verbatim}
\end{Usage}
\begin{Arguments}
\begin{ldescription}
\item[\code{x}] data  matrix. Missing values (NAs) are not allowed.

\item[\code{wt}] A vector of weights for each case: these are treated as if the case \code{i}
actually occurred \code{wt[i]} times.

\item[\code{cor}] Flag to choose between returning the correlation (\code{cor = TRUE}) or
covariance (\code{cor = FALSE}) matrix.

\item[\code{center}] a logical value or a numeric vector providing the location about which
the covariance is to be taken. If \code{center = FALSE}, no centering
is done; if \code{center = TRUE} the MLE of the location vector is used.

\item[\code{nu}] \sQuote{degrees of freedom} for the multivariate t distribution. Must exceed
2 (so that the covariance matrix is finite).

\item[\code{maxit}] Maximum number of iterations in fitting.

\item[\code{tol}] Convergence tolerance for fitting.

\end{ldescription}
\end{Arguments}
\begin{Value}
A list with the following components

\begin{ldescription}
\item[\code{cov}] the fitted covariance matrix.

\item[\code{center}] the estimated or specified location vector.

\item[\code{wt}] the specified weights: only returned if the \code{wt} argument was given.

\item[\code{n.obs}] the number of cases used in the fitting.

\item[\code{cor}] the fitted correlation matrix: only returned if \code{cor = TRUE}.

\item[\code{call}] The matched call.

\item[\code{iter}] The number of iterations used.

\end{ldescription}
\end{Value}
\begin{References}\relax
J. T. Kent, D. E. Tyler and Y. Vardi (1994)
A curious likelihood identity for the multivariate t-distribution.
\emph{Communications in Statistics---Simulation and Computation}
\bold{23}, 441--453.

Venables, W. N. and Ripley, B. D. (1999)
\emph{Modern Applied Statistics with S-PLUS.} Third
Edition. Springer.
\end{References}
\begin{SeeAlso}\relax
\code{\LinkA{cov}{cov}}, \code{\LinkA{cov.wt}{cov.wt}}, \code{\LinkA{cov.mve}{cov.mve}}
\end{SeeAlso}
\begin{Examples}
\begin{ExampleCode}
cov.trob(stackloss)
\end{ExampleCode}
\end{Examples}

