A test for k sample Behrens-Fisher problem in high dimensional data

TL;DR

This paper introduces a new statistical test for the k-sample Behrens-Fisher problem in high-dimensional data, showing improved power over existing tests, especially with unbalanced sample sizes, through theoretical and numerical analysis.

Contribution

A novel test statistic for high-dimensional k-sample Behrens-Fisher problem that outperforms existing tests in power, particularly with unbalanced samples.

Findings

Proposed test has higher power in unbalanced sample scenarios.

Theoretical analysis confirms the asymptotic superiority of the new test.

Numerical studies demonstrate improved size and power performance.

Abstract

In this paper, the $k$ sample Behrens-Fisher problem is investigated in high dimensional setting. We propose a new test statistic and demonstrate that the proposed test is expected to have more powers than some existing test especially when sample sizes are unbalanced. We provide theoretical investigation as well as numerical studies on both sizes and powers of the proposed tests and existing test. Both theoretical comparison of the asymptotic power functions and numerical studies show that the proposed test tends to have more powers than existing test in many cases of unbalanced sample sizes.