Two sample tests for high-dimensional covariance matrices

TL;DR

This paper introduces two novel nonparametric tests for assessing the equality of high-dimensional covariance matrices, effective in large p small n scenarios and applicable to gene ontology data.

Contribution

It develops two tests for high-dimensional covariance matrices that work without parametric assumptions and handle large p small n situations.

Findings

Tests are effective in high-dimensional settings

Applicable to gene ontology covariance analysis

Surpass traditional likelihood ratio tests

Abstract

We propose two tests for the equality of covariance matrices between two high-dimensional populations. One test is on the whole variance--covariance matrices, and the other is on off-diagonal sub-matrices, which define the covariance between two nonoverlapping segments of the high-dimensional random vectors. The tests are applicable (i) when the data dimension is much larger than the sample sizes, namely the "large $p$, small $n$" situations and (ii) without assuming parametric distributions for the two populations. These two aspects surpass the capability of the conventional likelihood ratio test. The proposed tests can be used to test on covariances associated with gene ontology terms.