Asymptotic linear dependence and ellipse statistics for multivariate two-sample homogeneity test

TL;DR

This paper introduces a new depth-based nonparametric test for multivariate two-sample homogeneity, demonstrating its effectiveness through simulations and real data, with an asymptotic Chi-square distribution under the null.

Contribution

It proposes a novel depth-based test for multivariate two-sample problems with a known asymptotic distribution, enhancing nonparametric inference methods.

Findings

Test has Chi-square(1) asymptotic distribution under null hypothesis.

Simulations show high power and robustness.

Real-data applications confirm practical utility.

Abstract

Statistical depth, which measures the center-outward rank of a given sample with respect to its underlying distribution, has become a popular and powerful tool in nonparametric inference. In this paper, we investigate the use of statistical depth in multivariate two-sample problems. We propose a new depth-based nonparametric two-sample test, which has the Chi-square(1) asymptotic distribution under the null hypothesis. Simulations and real-data applications highlight the efficacy and practical value of the proposed test.