TWO-SAMPLE AND ANOVA TESTS FOR HIGH DIMENSIONAL MEANS

• 成果类型: Article
• 署名作者: Chen, Song Xi; Li, Jun; Zhong, Ping-Shou
• 署名单位: Peking University; Peking University; University System of Ohio; Kent State University; Kent State University Salem; Kent State University Kent; Michigan State University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/18-AOS1720
• 发表日期: 2019
• 页码: 1443-1474
• 关键词: higher criticism; matrices

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 nonsignal 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.