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| HAL : hal-00125670, version 1 |
| arXiv : math.ST/0701605 |
| DOI : 10.1007/978-3-540-72927-3_11 |
| Fiche détaillée |  Récupérer au format |
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| Learning Theory 20th Annual Conference on Learning Theory, COLT 2007, San Diego, CA, USA; June 13-15, 2007. Proceedings, Nader H. Bshouty and Claudio Gentile (Ed.) (2007) 127-141 |
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| Resampling-based confidence regions and multiple tests for a correlated random vector |
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| Sylvain Arlot 1Gilles Blanchard 2 |
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| (12/06/2007) |
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| We 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. |
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| 1 : | Laboratoire de Mathématiques d'Orsay (LM-Orsay) |
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CNRS : UMR8628 – Université Paris XI - Paris Sud |
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| 2 : | Fraunhofer FIRST.IDA (FHG FIRST.IDA) |
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Fraunhofer Institute |
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| 3 : | Unité Mathématique Informatique et Génome (MIG) |
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INRA |
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| Domaine | : | Mathématiques/Statistiques |
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| resampling – cross-validation – confidence region – multiple testing – concentration inequalities – resampled quantiles – gaussian vector – unknown correlations |
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| Liste des fichiers attachés à ce document : | ||||||||||
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| hal-00125670, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00125670 | |
| oai:hal.archives-ouvertes.fr:hal-00125670 | |
| Contributeur : Sylvain Arlot | |
| Soumis le : Lundi 22 Janvier 2007, 11:40:36 | |
| Dernière modification le : Jeudi 7 Février 2008, 21:57:50 | |
