A0543
Title: Reviving pseudo-inverses: Asymptotic properties of large dimensional generalized inverses with applications
Authors: Nestor Parolya - Delft University of Technology (Netherlands) [presenting]
Taras Bodnar - Stockholm University (Sweden)
Abstract: The purpose is to establish a connection between modern RMT and high-dimensional statistics combined with machine learning, which is referred to as 'high-dimensional statistical learning'. Subsequently, the recent results concerning the regularized learning/estimation of large covariance matrices are presented using (Moore-Penrose) pseudoinverse and Tikhonov regularization combined with statistical shrinkage techniques. Findings contribute to constructing improved shrinkage estimators for the precision matrix, particularly in scenarios where the number of variables p is comparable to the sample size $n$, resulting in $p/n$ converging to a constant $c>1$ (singular sample covariance matrix). A real-data application in finance is concluded by, demonstrating the superiority of the proposed methods over benchmarks like nonlinear shrinkage and cross-validation techniques in machine learning.
