Fit zero mean multivariate t-distribution

Description

estimate the parameters Sigma, m and v of the multivariate t-distribution with zero expectation.

Usage

1
estimateSigmaMV(y,maxIter=100,epsilon=0.000001,verbose=FALSE)

Arguments

y

data matrix

maxIter

maximum number of iterations

epsilon

convergence criteria

verbose

print computation info or not

Details

The multivariate t-distribution is parametrized as:

y|c ~ N(mu,c*Sigma)

c ~ InvGamma(m/2,m*v/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)=b^a exp{-b/x} x^{-a-1} /Gamma(a)

In this application mu equals zero, and m is the degrees of freedom.

Value

Sigma

Estimated covariance matrix for y

m

Estimated shape parameter for inverse-gamma prior for gene variances

v

Estimated scale parameter for inverse-gamma prior for gene variances

converged

T if the EM algorithms converged

iter

Number of iterations

modS2

Moderated estimator of gene-specific variances

histLogS2

Histogram of log(s2) where s2 is the ordinary variance estimator

fittedDensityLogS2

The fitted density for log(s2)

Author(s)

Magnus Astrand

References

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

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

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

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

See Also

estimateSigma