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

作者：Arlot Sylvain^*; Blanchard Gilles; Roquain Etienne

来源：Annals of Statistics, 2010, 38(1): 83-99.

DOI：10.1214/08-AOS668

• Family-wise error
• multiple testing
• high-dimensional data
• nonasymptotic error control
• resampling
• resampled quantile

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.

• 出版日期2010-2
• 单位INRIA