A new V-fold type procedure based on robust tests

Lucien Birgé 1 Nelo Magalhães 1, 2, 3 Pascal Massart 2, 3
3 SELECT - Model selection in statistical learning
Inria Saclay - Ile de France, LMO - Laboratoire de Mathématiques d'Orsay, CNRS - Centre National de la Recherche Scientifique : UMR
Abstract : We define a general V-fold cross-validation type method based on robust tests, which is an extension of the hold-out defined by Birgé [7, Section 9]. We give some theoretical results showing that, under some weak assumptions on the considered statistical procedures , our selected estimator satisfies an oracle type inequality. We also introduce a fast algorithm that implements our method. Moreover we show in our simulations that this V-fold performs generally well for estimating a density for different sample sizes, and can handle well-known problems, such as binwidth selection for histograms or bandwidth selection for kernels. We finally provide a comparison with other classical V-fold methods and study empirically the influence of the value of V on the risk.
Type de document :
Pré-publication, Document de travail
2015
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Contributeur : Nelo Magalhães <>
Soumis le : lundi 15 juin 2015 - 15:19:26
Dernière modification le : lundi 29 mai 2017 - 14:24:28
Document(s) archivé(s) le : mardi 25 avril 2017 - 08:14:06

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  • HAL Id : hal-01163771, version 1
  • ARXIV : 1506.04692

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Lucien Birgé, Nelo Magalhães, Pascal Massart. A new V-fold type procedure based on robust tests. 2015. <hal-01163771>

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