A new test statistic using interpoint distances is proposed to address the two‐sample problem for multivariate populations. The test statistic compares univariate distributions of within and between samples pairwise distances using a Cramér‐von Mises‐type statistic. The critical values are approximated by means of a permutation procedure and the regularity conditions required to ensure the consistency of the test are established. Unlike other two‐sample procedures, our approach compares the whole distributions of interpoint distances instead of just a few moments, thus obtaining a higher capability to detect differences in their shape or in other moments. An extensive simulation study and experiments with real data sets considered in related papers show a satisfactory performance of the proposed test under a range of alternative distributions. Compared to other two‐sample tests based on interpoint distances, the experiments reveal a more robust behavior in a high‐dimensional setting, being one of the most powerful tests under both location and scales changes.

中文翻译：

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两样本同质性测试：一种基于比较点间距离分布的程序

提出了一种新的使用点间距离的检验统计量，以解决多变量总体的两样本问题。检验统计量使用Cramér-vonMises型统计量比较样本内和样本间距离之间的单变量分布。通过置换程序估算临界值，并建立确保测试一致性所需的规则性条件。与其他两个样本过程不同，我们的方法比较了点间距离的整个分布，而不是仅仅比较几个瞬间，从而获得了更高的检测其形状或其他瞬间差异的能力。广泛的模拟研究和相关论文中考虑的真实数据的实验表明，在一系列替代分布下，该测试的性能令人满意。