On testing the equality of high dimensional mean vectors with unequal covariance matrices

TL;DR

This paper introduces a new test for comparing high-dimensional mean vectors with unequal covariances, demonstrating superior performance in large dimensions compared to existing methods.

Contribution

A novel test statistic for high-dimensional mean vector equality with unequal covariances, with derived asymptotic distributions and improved performance in large dimensions.

Findings

The proposed test outperforms existing tests in high-dimensional settings.

Asymptotic distributions under null and alternative hypotheses are derived.

The new test shows better power in large-dimensional cases.

Abstract

In this article, we focus on the problem of testing the equality of several high dimensional mean vectors with unequal covariance matrices. This is one of the most important problem in multivariate statistical analysis and there have been various tests proposed in the literature. Motivated by \citet{BaiS96E} and \cite{ChenQ10T}, a test statistic is introduced and the asymptomatic distributions under the null hypothesis as well as the alternative hypothesis are given. In addition, it is compared with a test statistic recently proposed by \cite{SrivastavaK13Ta}. It is shown that our test statistic performs much better especially in the large dimensional case.