estimateSigma {plw} | R Documentation

## 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

### 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

[Package plw version 1.0.0 Index]