Open Access
February 2010 Some nonasymptotic results on resampling in high dimension, I: Confidence regions
Sylvain Arlot, Gilles Blanchard, Etienne Roquain
Ann. Statist. 38(1): 51-82 (February 2010). DOI: 10.1214/08-AOS667


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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Sylvain Arlot. Gilles Blanchard. Etienne Roquain. "Some nonasymptotic results on resampling in high dimension, I: Confidence regions." Ann. Statist. 38 (1) 51 - 82, February 2010.


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

zbMATH: 1180.62066
MathSciNet: MR2589316
Digital Object Identifier: 10.1214/08-AOS667

Primary: 62G15
Secondary: 62G09

Keywords: Concentration inequalities , Confidence regions , cross-validation , High-dimensional data , nonasymptotic error control , resampled quantile , Resampling

Rights: Copyright © 2010 Institute of Mathematical Statistics

Vol.38 • No. 1 • February 2010
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