CRAMER-TYPE MODERATE DEVIATIONS FOR STUDENTIZED TWO-SAMPLE U-STATISTICS WITH APPLICATIONS

• 成果类型: Article
• 署名作者: Chang, Jinyuan; Shao, Qi-Man; Zhou, Wen-Xin
• 署名单位: Southwestern University of Finance & Economics - China; University of Melbourne; Chinese University of Hong Kong; Princeton University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/15-AOS1375
• 发表日期: 2016
• 页码: 1931-1956
• 关键词: false discovery rate; High-dimensional Data; LIMIT-THEOREMS; t-tests; bootstrap

摘要

Two-sample U-statistics are widely used in a broad range of applications, including those in the fields of biostatistics and econometrics. In this paper, we establish sharp Cramer-type moderate deviation theorems for Studentized two-sample U-statistics in a general framework, including the two-sample t-statistic and Studentized Mann Whitney test statistic as prototypical examples. In particular, a refined moderate deviation theorem with second-order accuracy is established for the two-sample t-statistic. These results extend the applicability of the existing statistical methodologies from the one-sample t-statistic to more general nonlinear statistics. Applications to two-sample large-scale multiple testing problems with false discovery rate control and the regularized bootstrap method are also discussed.