Two-Sample Tests Based on Data Depth

In this paper, we focus on the homogeneity test that evaluates whether two multivariate samples come from the same distribution. This problem arises naturally in various applications, and there are many methods available in the literature. Based on data depth, several tests have been proposed for this problem but they may not be very powerful. In light of the recent development of data depth as an important measure in quality assurance, we propose two new test statistics for the multivariate two-sample homogeneity test. The proposed test statistics have the same chi(2)(1) asymptotic null distribution. The generalization of the proposed tests into the multivariate multisample situation is discussed as well. Simulations studies demonstrate the superior performance of the proposed tests. The test procedure is illustrated through two real data examples.

Automated summary

This paper focuses on the homogeneity test for evaluating whether two multivariate samples come from the same distribution. Various methods have been proposed in the literature, but they may not be very powerful. Based on data depth, two new test statistics are proposed for the multivariate two-sample homogeneity test, which have the same chi(2)(1) asymptotic null distribution. The generalization of these tests into the multivariate multisample situation is also discussed. Simulation studies demonstrate the superior performance of the proposed tests, and the test procedure is illustrated through two real data examples.