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Data depth has been applied as a nonparametric measurement for rankingmultivariate samples. In this paper, we focus on homogeneity tests to assesswhether two multivariate samples are from the same distribution. There are manydata depth-based tests for this problem, but they may not be very powerful, orhave unknown asymptotic distributions, or have slow convergence rates toasymptotic distributions. Given the recent development of data depth as animportant measure in quality assurance, we propose three new test statisticsfor multivariate two-sample homogeneity tests. The proposed minimum teststatistics have simple asymptotic half-normal distribution. We also discuss thegeneralization of the proposed tests to multiple samples. The simulation studydemonstrates the superior performance of the proposed tests. The test procedureis illustrated by two real data examples.

Multivariate two-sample test statistics based on data depth