Interpoint distance based two sample tests in high dimension

In this paper, we study a class of two sample test statistics based on inter-point distances in the high dimensional and low/medium size setting. Our include well-known energy distance maximum mean discrepancy with Gaussian Laplacian kernels, critical values are obtained via permutations. We show that all these tests inconsistent when distributions correspond to same marginal but differ other aspects distributions. The mainly target differences between means variances, whereas L1-distance can capture difference theory sheds new light limitation tests, impact different metrics, behavior permutation dimension. Some simulation results real data illustration also presented corroborate our theoretical findings.