Speaker： Liping Zhu（Renmin University of China）

Time：2019-05-09,16:30

Location： Conference Room 105 at Experiment Building at Haiyun Campus

Abstract: We propose a robust nonparametric two-sample test, which generalizes the Cram\'er-von Mises test through projections, to test for equality of two distributions in high dimensions. The population version of our proposed generalized Cram\'er-von Mises statistic is nonnegative equals zero if only if the two distributions are identical, ensuring that our proposed test is consistent against all fixed alternatives. In addition, our proposed test statistic has an explicit form is completely free of tuning parameters. It requires no moment conditions hence is robust to the presence of outliers heavy-tail observations. We study the asymptotic behaviors of our proposed test under both the ``large sample size, fixed dimension" the ``fixed sample size, large dimension" paradigms. In the former paradigm, we show that the asymptotic power of our proposed test does not depend on the size ratio of the two random samples. This ensures that our proposed test can be readily applied to imbalanced samples. In the latter paradigm, we observe that, surprisingly, the two distributions are equal if only if their first two moments are equal. Therefore, we suggest to tailor our proposed test to detect location shifts scale differences, which further enhances the power performance of our proposed test significantly. Numerical studies confirm that our proposals are superior to many existing tests in high dimensional two-sample test problems.