Shrinkage and Spectral Filtering of Correlation Matrices: a Comparison via the Kullback–leibler Distance∗

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.