学术报告（ 陈松蹊 12.24）
Two-Sample and ANOVA Tests for High Dimensional Means
摘 要：
This paper considers testing the equality of two high dimensional means. Two approaches are utilized to formulate $L_2$-type tests for better power performance when the two high dimensional mean vectors differ only in sparsely populated coordinates and the differences are faint. One is to conduct thresholding to remove the non-signal bearing dimensions for variance reduction of the test statistics. The other is to transform the data via the precision matrix for signal enhancement. It is shown that the thresholding and data transformation lead to attractive detection boundaries for the tests.
Furthermore, we demonstrate explicitly the effects of precision matrix estimation on the detection boundary for the test with thresholding and data transformation. Extension to multi-sample ANOVA tests is also investigated. Numerical studies are performed to confirm the theoretical findings and demonstrate the practical implementations.
个人简介：
陈松蹊教授，国家特聘专家，北京大学讲席教授，北大光华管理学院商务统计与经济计量系联合系主任、北京大学统计科学中心联席主任，美国科学促进会会士（AAAS Fellow），数理统计学会(Institute of Mathematical Statistics) 会士（fellow)，美国统计学会会士（ASA fellow），国际统计学会 (International Statistics Institute) 当选会员 （elected member），国际数理统计学会 (IMS) 理事会常务理事( Council member)。他现在是The Annals of Statistics(统计年鉴) 副主编 (自2010年）；Journal of Business and Economic Statistics 副主编 （自2013年）；曾任Statistics and Its Interface 的联席主编（2010-2013）。
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华南统计科学研究中心
2018/12/01
