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

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

Maximal spaces with given rate of convergence for thresholding algorithms


Code(s) de Classification MSC:

Résumé: The goal of this paper is to address the following question : given an estimation method and a prescribed rate of convergence for a given loss function what is the maximal space over which this rate is attained. We will discuss here the existence and the nature of maximal spaces in the context of non linear methods based on thresholding procedures. It turns out that the maximal spaces in this setting will coincide with known smoothness classes. These classes also appear to play an essential role in approximation theory. We mainly investigate losses which can be expressed as weighted $l_p$-norms of wavelet coefficents (such as particular Besov norms), or the more difficult case of $L_p$-norms.

Mots Clés: Maximal space ; shrinkage method ; non linear approximation

Date: 1999-10-28

Prépublication numéro: PMA-537