A0314
Title: Resurrecting pseudoinverse: Asymptotic properties of large Moore-Penrose inverse with applications
Authors: Nestor Parolya - Delft University of Technology (Netherlands) [presenting]
Taras Bodnar - Stockholm University (Sweden)
Abstract: High-dimensional asymptotic properties of the Moore-Penrose inverse of the sample covariance matrix are derived, i.e., when the number of variables p is larger than the sample size n. The convergence results related to the traces of weighted moments of the Moore-Penrose inverse matrix, which involve both its eigenvalues and eigenvectors, are proved. Previous findings are extended in several directions: (i) first, the population covariance matrix is not assumed to be a multiple of the identity; (ii) second, the assumptions of normality are not used in the derivation, only the existence of the 4th moments is required; (iii) third, the asymptotic properties of the weighted moments are derived under the high-dimensional asymptotic regime, when both p and n approaches infinity such that p/n tends to a constant c>1. The findings allow the construction of the optimal linear shrinkage estimators for large precision matrix, beta-vector in the high-dimensional linear models and minimum L2 portfolio. Finally, the finite sample properties of the derived theoretical results are investigated via an extensive simulation study.
