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February 2010 Some nonasymptotic results on resampling in high dimension, II: Multiple tests
Sylvain Arlot, Gilles Blanchard, Etienne Roquain
Ann. Statist. 38(1): 83-99 (February 2010). DOI: 10.1214/08-AOS668


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.


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Sylvain Arlot. Gilles Blanchard. Etienne Roquain. "Some nonasymptotic results on resampling in high dimension, II: Multiple tests." Ann. Statist. 38 (1) 83 - 99, February 2010.


Published: February 2010
First available in Project Euclid: 31 December 2009

zbMATH: 1181.62055
MathSciNet: MR2589317
Digital Object Identifier: 10.1214/08-AOS668

Primary: 62G10
Secondary: 62G09

Keywords: Family-wise error , High-dimensional data , multiple testing , nonasymptotic error control , resampled quantile , Resampling

Rights: Copyright © 2010 Institute of Mathematical Statistics


Vol.38 • No. 1 • February 2010
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