Asymptotic testing of covariance separability for matrix elliptical data

TL;DR

This paper introduces a new asymptotic test for covariance matrix separability applicable to a broad class of matrix elliptical distributions, including Gaussian and t-distributions, with good power and computational efficiency.

Contribution

It proposes a novel, fast asymptotic test for covariance separability that is valid under wide elliptical models and does not assume specific covariance structures.

Findings

Test performs well with heavy-tailed distributions

Both test versions have high power

Competes with Gaussian likelihood ratio test for normal data

Abstract

We propose a new asymptotic test for the separability of a covariance matrix. The null distribution is valid in wide matrix elliptical model that includes, in particular, both matrix Gaussian and matrix $t$-distribution. The test is fast to compute and makes no assumptions about the component covariance matrices. An alternative, Wald-type version of the test is also proposed. Our simulations reveal that both versions of the test have good power even for heavier-tailed distributions and can compete with the Gaussian likelihood ratio test in the case of normal data.