Université Paris 6
Pierre et Marie Curie
Université Paris 7
Denis Diderot

CNRS U.M.R. 7599
``Probabilités et Modèles Aléatoires''

Maxiset for density estimation

Auteur(s):

Code(s) de Classification MSC:

Résumé: The problem of density estimation on $\mathbb{R}$ is concerned. Adopting the maxiset point of view, the aim of this paper is threefold. Firstly, we prove that the maxiset of any elitist rule is contained in the intersection of a Besov space and a weak Besov space. Secondly, we provide an adaptive procedure for which the maxiset is the largest one among elitist rules (ideal maxiset). Thirdly, we point out the significance of data-driven thresholds in estimation by comparing the maxisets of this last procedure with the procedure using data-driven thresholds proposed by Juditsky and Lambert-Lacroix.

Mots Clés: nonparametric estimation ; minimax risk ; maximal spaces ; adaptive procedure ; thresholding rules ; Besov spaces and weak Besov spaces

Date: 2003-05-23

Prépublication numéro: PMA-822