PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Some nonasymptotic results on resampling in high dimension, I: Confidence regions
Sylvain Arlot, Gilles Blanchard and Etienne Roquain
Annals of Statistics Volume 38, Number 1, pp. 51-82, 2010. ISSN 00905364

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Abstract

We study generalized bootstrap confidence regions for the mean of a random vector whose coordinates have an unknown dependency structure. The random vector is supposed to be either Gaussian or to have a symmetric and bounded distribution. The dimensionality of the vector can possibly be much larger than the number of observations and we focus on a nonasymptotic control of the confidence level, following ideas inspired by recent results in learning theory. We consider two approaches, the first based on a concentration principle (valid for a large class of resampling weights) and the second on a resampled quantile, specifically using Rademacher weights. Several intermediate results established in the approach based on concentration principles are of interest in their own right. We also discuss the question of accuracy when using Monte Carlo approximations of the resampled quantities.

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EPrint Type:Article
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Computational, Information-Theoretic Learning with Statistics
Learning/Statistics & Optimisation
Theory & Algorithms
ID Code:3259
Deposited By:Gilles Blanchard
Deposited On:02 February 2008

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