Multivariate two-sample test statistics based on data depth

TL;DR

This paper introduces three new data depth-based test statistics for assessing whether two multivariate samples originate from the same distribution, demonstrating superior performance through simulations and real data examples.

Contribution

The paper proposes three novel multivariate two-sample homogeneity tests with simple asymptotic distributions, improving power and convergence over existing methods.

Findings

Proposed tests have simple asymptotic half-normal distribution.

Simulation shows superior performance of the new tests.

Real data examples validate the effectiveness of the methods.

Abstract

Data depth has been applied as a nonparametric measurement for ranking multivariate samples. In this paper, we focus on homogeneity tests to assess whether two multivariate samples are from the same distribution. There are many data depth-based tests for this problem, but they may not be very powerful, or have unknown asymptotic distributions, or have slow convergence rates to asymptotic distributions. Given the recent development of data depth as an important measure in quality assurance, we propose three new test statistics for multivariate two-sample homogeneity tests. The proposed minimum test statistics have simple asymptotic half-normal distribution. We also discuss the generalization of the proposed tests to multiple samples. The simulation study demonstrates the superior performance of the proposed tests. The test procedure is illustrated by two real data examples.