PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Resampling-based confidence regions and multiple tests for a correlated random vector
Sylvain Arlot, Gilles Blanchard and Etienne Roquain
In: Learning Theory Lecture Notes in Artifical Intelligence , 4539 . (2007) Springer , Berlin , pp. 127-141. ISBN 978-3-540-72925-9

Abstract

We study generalized bootstrapped confidence regions for the mean of a random vector whose coordinates have an unknown dependence structure, with 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 boostrapped quantile. The first one allows us to deal with a very large class of resampling weights while our results for the second are restricted to Rademacher weights. However, the second method seems more accurate in practice. Our results are motivated by multiple testing problems, and we show on simulations that our procedures are better than the Bonferroni procedure (union bound) as soon as the observed vector has sufficiently correlated coordinates.

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EPrint Type:Book Section
Additional Information:Proceedings of COLT 2007
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Computational, Information-Theoretic Learning with Statistics
ID Code:3377
Deposited By:Sylvain Arlot
Deposited On:09 February 2008