A nonparametric two-sample test applicable to high dimensional data

The multivariate two-sample testing problem has been well investigated in the literature, and several parametric and nonparametric methods are available for it. However, most of these two-sample tests perform poorly for high dimensional data, and many of them are not applicable when the dimension of the data exceeds the sample size. In this article, we propose a multivariate two-sample test that can be conveniently used in the high dimension low sample size setup. Asymptotic results on the power properties of our proposed test are derived when the sample size remains fixed, and the dimension of the data grows to infinity. We investigate the performance of this test on several high-dimensional simulated and real data sets, and demonstrate its superiority over several other existing two-sample tests. We also study some theoretical properties of the proposed test for situations when the dimension of the data remains fixed and the sample size tends to infinity. In such cases, it turns out to be asymptotically distribution-free and consistent under general alternatives.