Shrinkage and spectral filtering of correlation matrices: a comparison via the Kullback-Leibler distance

Details Shrinkage and spectral filtering of correlation matrices: a comparison via the Kullback-Leibler distance Shrinkage and spectral filtering of correlation matrices: a comparison via the Kullback-Leibler distance

2007-10-02

arxiv.org/abs/0710.0576v1

Acta Phys. Pol. B 38 (13), 4079-4088 (2007)

Physics

Data Analysis, Statistics and Probability

11 pages, 4 figures, Presented at the Workshop "Random Matrix Theory: From Fundamental Physics To Application", Krakow, Poland

Scientific paper

The problem of filtering information from large correlation matrices is of great importance in many applications. We have recently proposed the use of the Kullback-Leibler distance to measure the performance of filtering algorithms in recovering the underlying correlation matrix when the variables are described by a multivariate Gaussian distribution. Here we use the Kullback-Leibler distance to investigate the performance of filtering methods based on Random Matrix Theory and on the shrinkage technique. We also present some results on the application of the Kullback-Leibler distance to multivariate data which are non Gaussian distributed.

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