HAL: hal-00634404, version 1

DOI: 10.1007/s00365-009-9062-2

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Constructive Approximation 31, 2 (2010) 195-229

Maxisets for model selection

Florent Autin 1, Erwan Le Pennec 2, Jean-Michel Loubes 3, Vincent Rivoirard 4, 5

(2010)

We address the statistical issue of determining the maximal spaces (maxisets) where model selection procedures attain a given rate of convergence. By considering first general dictionaries, then orthonormal bases, we characterize these maxisets in terms of approximation spaces. These results are illustrated by classical choices of wavele model collections. For each of them, the maxisets are described in terms of functional spaces. We take a special case of the issue of calculability and measure the induced loss of performance in terms of maxisets.

1:	Centre de Mathématiques et Informatique (CMI)
	Université de Provence - Aix-Marseille I
2:	Laboratoire de Probabilités et Modèles Aléatoires (LPMA)
	CNRS : UMR7599 – Université Pierre et Marie Curie [UPMC] - Paris VI – Université Paris VII - Paris Diderot
3:	Institut de Mathématiques de Toulouse (IMT)
	Université Paul Sabatier [UPS] - Toulouse III – Université Toulouse le Mirail - Toulouse II – Université des Sciences Sociales - Toulouse I – Institut National des Sciences Appliquées (INSA) - Toulouse – CNRS : UMR5219
4:	Laboratoire de Mathématiques d'Orsay (LM-Orsay)
	CNRS : UMR8628 – Université Paris XI - Paris Sud
5:	Département de Mathématiques et Applications (DMA)
	CNRS : UMR8553 – Ecole normale supérieure de Paris - ENS Paris

Subject

:

Mathematics/Statistics Statistics/Statistics Theory

Keyword(s): Approximation spaces – Approximation theory – Besov spaces – Estimation – Maxiset – Model selection – Rates of convergence

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From: Vincent Rivoirard <>

Submitted on: Friday, 21 October 2011 09:25:26

Updated on: Friday, 28 October 2011 16:03:16