General linear hypothesis testing of high-dimensional mean vectors with unequal covariance matrices based on random integration

TL;DR

This paper proposes a new high-dimensional mean vector testing method using $L^2$-norm and random integration, with proven asymptotic distribution and verified advantages through simulations.

Contribution

It introduces a novel test statistic for high-dimensional mean vectors with unequal covariances based on random integration, expanding existing methodologies.

Findings

Asymptotic distribution derived for the proposed test statistic.

Numerical simulations demonstrate advantages over existing methods.

Effective for high-dimensional multi-sample mean testing with unequal covariances.

Abstract

This paper is devoted to the study of the general linear hypothesis testing (GLHT) problem of multi-sample high-dimensional mean vectors. For the GLHT problem, we introduce a test statistic based on $L^2$-norm and random integration method, and deduce the asymptotic distribution of the statistic under given conditions. Finally, the potential advantages of our test statistics are verified by numerical simulation studies and examples.