HAL : hal-00262478, version 2

arXiv : 0906.3124

DOI : 10.1214/08-EJS196

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Electronic Journal of Statistics 3 (2009) 557--624

Versions disponibles :

v1 (11-03-2008)

v2 (17-06-2009)

Model selection by resampling penalization

Sylvain Arlot 1, 2

(06/2009)

In this paper, a new family of resampling-based penalization procedures for model selection is defined in a general framework. It generalizes several methods, including Efron's bootstrap penalization and the leave-one-out penalization recently proposed by Arlot (2008), to any exchangeable weighted bootstrap resampling scheme. In the heteroscedastic regression framework, assuming the models to have a particular structure, these resampling penalties are proved to satisfy a non-asymptotic oracle inequality with leading constant close to 1. In particular, they are asympotically optimal. Resampling penalties are used for defining an estimator adapting simultaneously to the smoothness of the regression function and to the heteroscedasticity of the noise. This is remarkable because resampling penalties are general-purpose devices, which have not been built specifically to handle heteroscedastic data. Hence, resampling penalties naturally adapt to heteroscedasticity. A simulation study shows that resampling penalties improve on V-fold cross-validation in terms of final prediction error, in particular when the signal-to-noise ratio is not large.

1 :	Laboratoire d'informatique de l'école normale supérieure (LIENS)
	CNRS : UMR8548 – Ecole normale supérieure de Paris - ENS Paris
2 :	WILLOW (INRIA Rocquencourt)
	INRIA – Ecole normale supérieure de Paris - ENS Paris – Ecole des Ponts ParisTech – CNRS : UMR8548

Domaine

:

Mathématiques/Statistiques Statistiques/Théorie

Mots Clés : non-parametric statistics – resampling – exchangeable weighted bootstrap – model selection – penalization – non-parametric regression – adaptivity – heteroscedastic data – regressogram – histogram selection

hal-00262478, version 2

http://hal.archives-ouvertes.fr/hal-00262478

oai:hal.archives-ouvertes.fr:hal-00262478

Contributeur : Sylvain Arlot <>

Soumis le : Mercredi 17 Juin 2009, 11:28:29

Dernière modification le : Vendredi 19 Juin 2009, 11:55:57