Shrinkage and spectral filtering of correlation matrices: a comparison via the Kullback-Leibler distance
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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.
11 pages, 4 figures, Presented at the Workshop "Random Matrix Theory: From Fundamental Physics To Application", Krakow, Poland, May 3-5, 2007
11 pages, 4 figures, Presented at the Workshop "Random Matrix Theory: From Fundamental Physics To Application", Krakow, Poland, May 3-5, 2007