Two-sample tests for high-dimension, strongly spiked eigenvalue models

TL;DR

This paper develops new two-sample testing procedures for high-dimensional data under models with strongly spiked eigenvalues, providing theoretical properties and practical effectiveness.

Contribution

It introduces a general test statistic applicable to both SSE and NSSE models, with conditions for consistency, asymptotic normality, and an optimized test procedure for SSE.

Findings

Test statistic satisfies consistency and asymptotic normality conditions.

Optimality established for the test under the NSSE model.

Numerical results demonstrate the test's effectiveness.

Abstract

We consider two-sample tests for high-dimensional data under two disjoint models: the strongly spiked eigenvalue (SSE) model and the non-SSE (NSSE) model. We provide a general test statistic as a function of a positive-semidefinite matrix. We give sufficient conditions for the test statistic to satisfy a consistency property and to be asymptotically normal. We discuss an optimality of the test statistic under the NSSE model. We also investigate the test statistic under the SSE model by considering strongly spiked eigenstructures and create a new effective test procedure for the SSE model. Finally, we discuss the performance of the classifiers numerically.