A regularized profile likelihood approach to covariance matrix estimation

Abstract

Two new orthogonally equivariant estimators of the covariance matrix are proposed. The estimates of the population eigenvalues are isotonized maximum likelihood estimates of the modified profile likelihood obtained from the Wishart distribution, in one case, and of a penalized form of such a likelihood function, in the other, with a penalty that constrains the trace of the sample covariance matrix. Properties of these estimators are studied and numerical risk comparisons with six other well-known estimators are presented to demonstrate the robustness of the proposed estimators for various real and simulated covariance structures. (C) 2016 Elsevier B.V. All rights reserved.