\HeaderA{cov.wt}{Weighted Covariance Matrices}{cov.wt}
\keyword{multivariate}{cov.wt}
\begin{Description}\relax
Returns a list containing estimates of the weighted covariance matrix
and the mean of the data, and optionally of the (weighted) correlation
matrix.
\end{Description}
\begin{Usage}
\begin{verbatim}
cov.wt(x, wt = rep(1/nrow(x), nrow(x)), cor = FALSE, center = TRUE,
       method = c("unbiased", "ML"))
\end{verbatim}
\end{Usage}
\begin{Arguments}
\begin{ldescription}
\item[\code{x}] a matrix or data frame.  As usual, rows are observations and
columns are variables.
\item[\code{wt}] a non-negative and non-zero vector of weights for each
observation.  Its length must equal the number of rows of \code{x}.
\item[\code{cor}] a logical indicating whether the estimated correlation
weighted matrix will be returned as well.
\item[\code{center}] either a logical or a numeric vector specifying the
centers to be used when computing covariances.  If \code{TRUE}, the
(weighted) mean of each variable is used, if \code{FALSE}, zero is
used.  If \code{center} is numeric, its length must equal the number
of columns of \code{x}.
\item[\code{method}] string specifying how the result is scaled, see
\emph{Details} below.
\end{ldescription}
\end{Arguments}
\begin{Details}\relax
By default, \code{method = "unbiased"},
The covariance matrix is divided by one minus the sum of squares of
the weights, so if the weights are the default (\eqn{1/n}{}) the conventional
unbiased estimate of the covariance matrix with divisor \eqn{(n - 1)}{}
is obtained.  This differs from the behaviour in S-PLUS which
corresponds to \code{method = "ML"} and does not divide.
\end{Details}
\begin{Value}
A list containing the following named components:
\begin{ldescription}
\item[\code{cov}] the estimated (weighted) covariance matrix
\item[\code{center}] an estimate for the center (mean) of the data.
\item[\code{n.obs}] the number of observations (rows) in \code{x}.
\item[\code{wt}] the weights used in the estimation.  Only returned if given
as an argument.
\item[\code{cor}] the estimated correlation matrix.  Only returned if
\code{cor} is \code{TRUE}.
\end{ldescription}
\end{Value}
\begin{SeeAlso}\relax
\code{\LinkA{cov}{cov}} and \code{\LinkA{var}{var}}.
\end{SeeAlso}
\begin{Examples}
\begin{ExampleCode}
 (xy <- cbind(x = 1:10, y = c(1:3, 8:5, 8:10)))
 w1 <- c(0,0,0,1,1,1,1,1,0,0)
 cov.wt(xy, wt = w1) # i.e. method = "unbiased"
 cov.wt(xy, wt = w1, method = "ML", cor = TRUE)
\end{ExampleCode}
\end{Examples}

