plw (version 1.32.0)

estimateSigma: Fit zero mean multivariate t-distribution, known df

Description

Estimate the covariance matrix $Sigma$ of the multivariate t-distribution with zero expectation assuming the degrees of freedom is known.

Usage

estimateSigma(y, m, v, maxIter = 100, epsilon = 1e-06, verbose = FALSE)

Arguments

y

data matrix

m

degrees of freedom

v

scale parameter

maxIter

maximum number of iterations

epsilon

convergence criteria

verbose

print computation info or not

Value

Sigma

Estimated covariance matrix for y

iter

Number of iterations

Details

The multivariate t-distribution is parametrized as: $$y|c \sim N(\mu,c\Sigma)$$ $$c \sim \mbox{InvGamma}(m/2,m\nu/2)$$ Here $N$ denotes a multivariate normal distribution, $Sigma$ is a covariance matrix and $InvGamma(a,b)$ is the inverse-gamma distribution with density function $$f(x)=(\beta)^{\alpha} \exp\{-\beta/x\} x^{-\alpha-1}/\Gamma(\alpha)$$ In this application $mu$ equals zero, and m is the degrees of freedom.

References

Hastie, T., Tibshirani, R., and Friedman, J. (2001). The Elements of Statistical Learning, volume 1. Springer, first edition.

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

$A$strand, M. et al. (2007a). Improved covariance matrix estimators for weighted analysis of microarray data. Journal of Computational Biology, Accepted.

$A$strand, M. et al. (2007b). Empirical Bayes models for multiple-probe type arrays at the probe level. Bioinformatics, Submitted 1 October 2007.

See Also

estimateSigmaMV