SOME NONASYMPTOTIC RESULTS ON RESAMPLING IN HIGH DIMENSION, II: MULTIPLE TESTS

• 成果类型: Article
• 署名作者: Arlot, Sylvain; Blanchard, Gilles; Roquain, Etienne
• 署名单位: Universite PSL; Ecole Normale Superieure (ENS); Centre National de la Recherche Scientifique (CNRS); CNRS - Institute for Information Sciences & Technologies (INS2I); Inria; Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Sorbonne Universite; Universite Paris Cite
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/08-AOS668
• 发表日期: 2010
• 页码: 83-99
• 关键词: false discovery rate; randomization tests; bootstrap

摘要

In the context of correlated Multiple tests, we aim to nonasymptotically control the family-wise error rate (FWER) using resampling-type procedures. We observe repeated realizations of a Gaussian random vector in possibly high dimension and with an unknown covariance matrix, and consider the one- and two-sided multiple testing problem for the mean values of its coordinates. We address this problem by using the confidence regions developed in the companion paper [Ann. Statist. (2009), to appear], which lead directly to single-step procedures, these can then be improved using step-down algorithms, following an established general methodology laid down by Romano and Wolf [J. Amer Statist. Assoc. 100 (2005) 94-108]. This gives rise to several different procedures, whose performances are compared Using simulated data.