Asymptotic testing of covariance separability for matrix elliptical data

2026-01-23

AI Summary

This study addresses the problem of testing separability of covariance matrices for matrix-valued data following elliptical distributions. The authors propose an asymptotic test that requires no prior assumptions on the component covariance structures, extending applicability beyond the Gaussian setting to a broader class of heavy-tailed distributions, including matrix Gaussian and matrix t-distributions. By leveraging asymptotic theory, they construct a computationally efficient test statistic and develop a Wald-type alternative. Simulation studies demonstrate that the proposed method maintains high power under heavy-tailed scenarios and performs comparably to the classical likelihood ratio test in Gaussian settings. This work significantly generalizes existing covariance separability testing frameworks, which have been largely confined to Gaussian assumptions.

Technology Category

• Machine Learning: Matrix & Tensor Methods
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Search and Optimization: Non-convex Optimization

Application Category

• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

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.

Problem

• covariance separability
• matrix elliptical data
• asymptotic test
• Kronecker product
• hypothesis testing

Innovation

• covariance separability
• matrix elliptical distribution
• asymptotic test
• Wald-type test
• heavy-tailed distributions