Fit zero mean multivariate t-distribution, known df

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Description

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

Usage

1
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

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

iter

Number of iterations

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

estimateSigmaMV