A unified approach for covariance matrix estimation under Stein loss

TL;DR

This paper presents a unified decision-theoretic approach for estimating covariance matrices of multivariate Gaussian distributions under Stein loss, covering both invertible and non-invertible cases.

Contribution

It introduces a novel unified framework for covariance matrix estimation under Stein loss, applicable to both invertible and non-invertible matrices.

Findings

Develops a unified estimator for covariance matrices

Addresses both invertible and non-invertible cases

Provides theoretical analysis of estimator performance

Abstract

In this paper, we address the problem of estimating a covariance matrix of a multivariate Gaussian distribution, relative to a Stein loss function, from a decision theoretic point of view. We investigate the case where the covariance matrix is invertible and the case when it is non--invertible in a unified approach.