Efficiency of the V-fold model selection for localized bases

Fabien Navarro (1) , Adrien Saumard (1)

1 CREST - Centre de Recherche en Economie et Statistique [Bruz]

Many interesting functional bases, such as piecewise polynomials or wavelets, are examples of localized bases. We investigate the optimality of V-fold cross-validation and a variant called V-fold penalization in the context of the selection of linear models generated by localized bases in a heteroscedastic framework. It appears that while V-fold cross-validation is not asymptotically optimal when V is fixed, the V-fold penalization procedure is optimal. Simulation studies are also presented.

Mots clés: V-fold cross-validation; V-fold penalization; model selection; nonparametric regression; heteroscedastic noise; random design; wavelets

Domaines: Statistiques [math.ST]; Méthodologie [stat.ME]

Fabien Navarro, Adrien Saumard. Efficiency of the V-fold model selection for localized bases. 2017. ⟨hal-01505514v1⟩