\HeaderA{estimateSigma}{Fit zero mean multivariate t-distribution, known df}{estimateSigma}
\keyword{htest}{estimateSigma}
\keyword{models}{estimateSigma}
\keyword{design}{estimateSigma}
\begin{Description}\relax
Estimate the covariance matrix \eqn{\Sigma}{} of the multivariate t-distribution with zero expectation assuming the degrees of freedom is known.
\end{Description}
\begin{Usage}
\begin{verbatim}
estimateSigma(y, m, v, maxIter = 100, epsilon = 1e-06, verbose = FALSE)
\end{verbatim}
\end{Usage}
\begin{Arguments}
\begin{ldescription}
\item[\code{y}] data matrix
\item[\code{m}] degrees of freedom
\item[\code{v}] scale parameter
\item[\code{maxIter}] maximum number of iterations
\item[\code{epsilon}] convergence criteria
\item[\code{verbose}] print computation info or not
\end{ldescription}
\end{Arguments}
\begin{Details}\relax
The multivariate t-distribution is parametrized as:
\deqn{y|c \sim N(\mu,c\Sigma)}{}
\deqn{c \sim \mbox{InvGamma}(m/2,m\nu/2)}{}
Here \eqn{N}{} denotes a multivariate normal distribution, 
\eqn{\Sigma}{} is a covariance matrix and 
\eqn{\mbox{InvGamma}(\alpha,\beta)}{} is the inverse-gamma distribution with density function
\deqn{f(x)=(\beta)^{\alpha} \exp\{-\beta/x\} x^{-\alpha-1}/\Gamma(\alpha)}{}
In this application \eqn{\mu}{} equals zero, and m is the degrees of freedom.
\end{Details}
\begin{Value}
\begin{ldescription}
\item[\code{Sigma}] Estimated covariance matrix for y
\item[\code{iter}] Number of iterations
\end{ldescription}
\end{Value}
\begin{Author}\relax
Magnus \eqn{\mbox{\AA}}{}strand
\end{Author}
\begin{References}\relax
Hastie, T., Tibshirani, R., and Friedman, J. (2001). The Elements of Statistical Learning, volume 1. Springer, first edition.

Kristiansson, E., Sj\eqn{\mbox{\"o}}{}gren, A., Rudemo, M., Nerman, O. (2005). Weighted Analysis of Paired Microarray Experiments. Statistical Applications in Genetics and Molecular Biology 4(1)

\eqn{\mbox{\AA}}{}strand, M. et al. (2007a). Improved covariance matrix estimators for weighted analysis of microarray data. Journal of Computational Biology, Accepted.

\eqn{\mbox{\AA}}{}strand, M. et al. (2007b). Empirical Bayes models for multiple-probe type arrays at the probe level. Bioinformatics, Submitted 1 October 2007.
\end{References}
\begin{SeeAlso}\relax
estimateSigmaMV
\end{SeeAlso}

