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Journal Articles Annals of Statistics Year : 2010

Some nonasymptotic results on resampling in high dimension, II: Multiple tests

Abstract

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. 38 (2010) 51-82], 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.
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hal-03334948 , version 1 (05-09-2021)

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Sylvain Arlot, Gilles Blanchard, Etienne Roquain. Some nonasymptotic results on resampling in high dimension, II: Multiple tests. Annals of Statistics, 2010, 38 (1), pp.83-99. ⟨10.1214/08-AOS668⟩. ⟨hal-03334948⟩
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