Estimation of large covariance matrices via free deconvolution: computational and statistical aspects

05/09/2023

∙

by   Reda Chhaibi, et al.

∙

0

∙

share

The estimation of large covariance matrices has a high dimensional bias. Correcting for this bias can be reformulated via the tool of Free Probability Theory as a free deconvolution. The goal of this work is a computational and statistical resolution of this problem. Our approach is based on complex-analytic methods methods to invert S-transforms. In particular, one needs a theoretical understanding of the Riemann surfaces where multivalued S transforms live and an efficient computational scheme.