  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.
