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: 20th conference on Learning Theory (COLT 2007), 13-15 June 2007, San Diego, CA, USA.

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. %, and we %observe $n$ i.i.d copies of it. %The confidence regions are built %using a data-dependent threshold based on a weighted bootstrap %procedure. 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:Conference or Workshop Item (Paper)
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Computational, Information-Theoretic Learning with Statistics
Learning/Statistics & Optimisation
Theory & Algorithms
ID Code:3257
Deposited By:Gilles Blanchard
Deposited On:02 February 2008