New two‐sample test utilizing interpoint distance discrepancy

Abstract

In this paper, we propose a novel two‐sample test for multivariate sample space. The test statistic calculates the mean of absolute difference of average interpoint distance. We utilize a permutation procedure to establish the critical value for the test. Through comprehensive simulation studies, we compare the performance of our proposed test with that of the K‐nearest neighbour test and the energy test. The results demonstrate that our proposed test exhibits advantages over the other two tests, particularly in high‐dimensional sample spaces. This superiority is further validated by its application to UCR time series datasets.