MAXISETS FOR MODEL SELECTION

Florent Autin (1) , Erwan Le Pennec (2) , Jean-Michel Loubes (3) , Vincent Rivoirard (4, 5, 6)

1 LATP - Laboratoire d'Analyse, Topologie, Probabilités
2 LPMA - Laboratoire de Probabilités et Modèles Aléatoires
3 IMT - Institut de Mathématiques de Toulouse UMR5219
4 LM-Orsay - Laboratoire de Mathématiques d'Orsay
5 UFR de Mathematiques
6 DMA - Département de Mathématiques et Applications - ENS Paris

We address the statistical issue of determining the maximal spaces (maxisets) where model selection procedures attain a given rate of convergence. We first prove that the answer lies in the approximation theory and we characterize these maxisets in terms of approximation spaces. This result is exemplified by three classical choices of model collections. For each of them, the corresponding maxisets are described in term of classical functional spaces. We take a special care of the issue of calculability and measure the induced loss of performance in terms of maxisets.

Mots clés: approximations spaces; approximation theory; Besov spaces; estimation; maxiset; model selection; rates of convergence

Domaines: Théorie [stat.TH]

Florent Autin, Erwan Le Pennec, Jean-Michel Loubes, Vincent Rivoirard. MAXISETS FOR MODEL SELECTION. 2008. ⟨hal-00259253v2⟩