Resampling-based confidence regions and multiple tests for a correlated random vector

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dc.creatorArlot, Sylvain
dc.creatorBlanchard, Gilles
dc.creatorRoquain, Etienne
dc.date2007-01-22
dc.date.accessioned2026-07-07T09:19:08Z
dc.date.available2026-07-07T09:19:08Z
dc.descriptionWe derive non-asymptotic confidence regions for the mean of a random vector whose coordinates have an unknown dependence structure. 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 approach and the second on a direct boostrapped quantile approach. The first one allows 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.
dc.descriptionsubmitted to COLT
dc.identifierhttps://arxiv.org/abs/math/0701605
dc.identifierhttp://arxiv.org/abs/math/0701605
dc.identifierLearning Theory 20th Annual Conference on Learning Theory, COLT 2007, San Diego, CA, USA; June 13-15, 2007. Proceedings, Springer Berlin / Heidelberg (Ed.) (2007) 127-141
dc.identifierdoi:10.1007/978-3-540-72927-3_11
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/154281
dc.subjectStatistics Theory
dc.subject62G09 ; 62H15
dc.titleResampling-based confidence regions and multiple tests for a correlated random vector
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