A New Nonparametric Test for Two Sample Multivariate Location Problem with Application to Astronomy

Abstract

This paper provides a nonparametric test for the identity of two multivariate continuous distribution functions 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.

Keywords

• Nonparametric multivariate test
• combination of Wilcoxon rank-sum tests
• outliers
• large sample distribution
• astronomical data
• compatibility test