报告人: 王学钦

报告题目:Ball Divergence: Multivariate Imbalance Test

报告人简介:王学钦，中山大学数学学院和中山医学院双聘教授，博士生导师，中山大学统计学科带头人，中山大学华南统计科学研究中心执行主任，国家优秀青年基金获得者，教育部统计专业教指委委员。

报告摘要：Abstract:
Two-sample hypothesis testing is a classic and fundamental topic in statistics. It becomes a difficult and yet important problem with high dimensional data, and especially with imbalanced sample sizes. In this paper, we first introduce Ball Divergence, a novel measure of the difference between two probability measures in finite dimensional Banach space, and show that the Ball Divergence of two probability measures is zero if and only if these two probability measures are identical. Using Ball Divergence, we present a metric rank test procedure to detect the equality of distribution measures underlying independent samples. We show that this multivariate two sample test statistic is consistent with the BallDivergence,  and it converges to a mixture of \chi^2 distributions under the null hypothesis and a normal distribution under the alternative hypothesis. Importantly, we prove its consistency against a general alternative hypothesis. Even without the moment assumption, the test based on BallDivergence is robust to the heavy-tail data. Moreover, the result does not depend on the ratio of the two imbalanced sample sizes, ensuring that the test is robust and can be applied to imbalanced data. Numerical studies confirm that our test is superior to several existing tests in terms of Type I error and power. We conclude our paper with two applications of our method: one is for virtual screening in drug development process and the other is for genome wide expression analysis in hormone replacement therapy.

报告时间：2016年10月18日上午11：00--12：00.
报告地点：科技南楼702