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.

翻译：数据深度已被作为一种非参数度量用于多元样本的排序。本文聚焦于同质性检验，以评估两个多元样本是否来自同一分布。针对此问题存在许多基于数据深度的检验方法，但它们可能效力不足、渐近分布未知，或渐近分布收敛速度较慢。鉴于数据深度最近作为质量控制中的重要度量得到发展，本文提出了三种新的多元两样本同质性检验统计量。所提出的最小检验统计量具有简单的渐近半正态分布。我们还讨论了将所提检验推广至多样本的情形。模拟研究显示了所提检验的优越性能。通过两个真实数据实例说明了检验流程。