A new nonparametric test for two sample multivariate location problem with application to astronomy

TL;DR

This paper introduces a robust nonparametric test for comparing two multivariate distributions focusing on location differences, demonstrating improved power and applicability to astronomical data.

Contribution

It proposes a novel Wilcoxon rank-sum based test for multivariate location differences that is resistant to outliers and validated through simulations and astronomical data applications.

Findings

Test is unaffected by outliers.

Power increases with sample size and number of components.

Effective in real astronomical data analysis.

Abstract

This paper provides a nonparametric test for the identity of two multivariate continuous distribution functions (d.f.'s) when they differ in locations. The test uses Wilcoxon rank-sum statistics on distances between observations for each of the components and is unaffected by outliers. It is numerically compared with two existing procedures in terms of power. The simulation study shows that its power is strictly increasing in the sample sizes and/or in the number of components. The applicability of this test is demonstrated by use of two astronomical data sets on early-type galaxies.