A Note on High Dimensional Two Sample Mean Test

TL;DR

This paper introduces a new high-dimensional two-sample mean test that is scalar and shift invariant, with an expectation of zero under the null hypothesis, demonstrating strong theoretical and simulation-based performance.

Contribution

It proposes a novel test statistic for high-dimensional two-sample mean testing that is invariant and has a null expectation of zero, applicable to arbitrarily large dimensions.

Findings

The test performs well in theoretical analysis.

Simulation results confirm its effectiveness.

The test is invariant to scalar and shift transformations.

Abstract

In this paper, we propose a new scalar and shift transform invariant test statistic for the high-dimensional two-sample location test. The expectation of our test is exactly zero under the null hypothesis. And we allow the dimension could be arbitrary large. Theoretical results and simulation comparison show the good performance of our test.