Year: 2009
Type: article
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.
Source: The Annals of Statistics
Institutions: Centre National de la Recherche Scientifique, École Normale Supérieure - PSL, WILLOW: Vision par ordinateur incarnée, Université Pierre-et-Marie-Curie, Weierstrass Institute for Applied Analysis and Stochastics, Fraunhofer-Gesellschaft, Laboratoire de Probabilités et Modèles Aléatoires
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W2917480902