PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Non-asymptotic resampling-based confidence regions and multiple tests in high dimension
Sylvain Arlot, Gilles Blanchard and Etienne Roquain
Hal 2007.

Abstract

We study generalized bootstrapped confidence regions for the mean of a random vector whose coordinates have an unknown dependence structure. The dimensionality of the vector can possibly be much larger than the number of observations and we focus on a non-asymptotic control of the confidence level. The random vector is supposed to be either Gaussian or to have a symmetric bounded distribution. We consider two approaches, the first based on a concentration principle and the second on a direct bootstrapped quantile. The first one allows us to deal with a very large class of resampling weights while our results for the second are specific to Rademacher weights. We present an application of these results to the one-sided and two-sided multiple testing problem, in which we derive several resampling-based step-down procedures providing a non-asymptotic FWER control. We compare our different procedures in a simulation study, and we show that they can outperform Bonferroni's or Holm's procedures as soon as the observed vector has sufficiently correlated coordinates.

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EPrint Type:Article
Additional Information:Long version of a COLT 2007 published paper
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Computational, Information-Theoretic Learning with Statistics
ID Code:3378
Deposited By:Sylvain Arlot
Deposited On:09 February 2008