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

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

Thresholding algorithms, maxisets and well concentrated bases


Code(s) de Classification MSC:

Résumé: The aim of this paper is to synthetically analyse the performances of thresholding and wavelet estimation methods. To attain this aim we propose to describe the maximal sets where these methods attain a special rate of convergence. We connect these "maxisets" to other problems naturally arising in the context of non parametric estimation, as approximation theory or information reduction. A second part of the paper is devoted to isolate two very special properties especially shared by wavelet bases, which allow them to behave almost as in an hilbertian context even for $L_p$ risks.

Mots Clés: non parametric estimation ; denoising ; minimax rate of convergence ; oracle inequalities ; saturation spaces ; wavelet thresholding ; Besov spaces ; approximation methods

Date: 2000-09-11

Prépublication numéro: PMA-611