Testing for the Equality of Distributions in High Dimension

In this paper, we propose a new homogeneous test for two highdimensional random vectors.Our test is built on a new measure, the so-called characteristic distance, which can completely characterize the homogeneity of two distributions.The newly proposed metric has some desirable properties, for example, it possesses a clear and intuitive probabilistic interpretation, and can be used to address the high-dimensional distance inference.Theoretically, the limiting behaviors under the conventional fixed dimension and high-dimensional distance inference are thoroughly investigated.Simulation studies and real data analysis are presented to illustrate the finite-sample performance of the proposed test statistic.