A two-sample test for equality of distributions in high dimensions

：朱利平教授
：2019-05-09 16:30
：实验楼105

Speaker：Prof. Liping Zhu

            Renmin University of China

Title: A two-sample test for equality of distributions in high dimensions

Time：09 May 2019,16:30

Location： 海韵实验楼105

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.

Speaker Introduction：2006年于华东师范大学取得博士学位。入选教育部新世纪优秀人才计划以及万人计划青年拔尖人才计划等，并获得国家自然科学基金委“优秀青年基金”等资助。 朱利平教授一直从事统计理论以及应用研究。研究兴趣主要涉及半参数建模、高维数据分析、充分降维以及变量选择等领域。