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

CNRS U.M.R. 7599
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``Probabilités et Modèles Aléatoires''
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**Auteur(s): **

**Code(s) de Classification MSC:**

- 62G05 Estimation
- 62G07 Curve estimation (nonparametric regression, density estimation, etc.)
- 62G20 Asymptotic properties

**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*