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

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

Wavelet deconvolution in a periodic setting


Code(s) de Classification MSC:

Résumé: In this paper we present an inverse estimation procedure which combines Fourier analysis with Wavelet expansion. In the periodic setting, our method can be applied to the deconvolution of either a density or a regression function. The proposal is non-linear and does not require any prior knowledge of the smoothness class; it enjoys fast computation and is spatially adaptive. The applicability of the method ranges from ordinary smooth convolution (polynomial decay of the Fourier transform) to irregular convolution operators such as the convolution with a box-car. Further, we show that, up to a log factor, our estimator is optimal among a large class of target functions for a variety of $L^p$ loss functions.

Mots Clés: Adaptive estimation ; deconvolution ; density estimation ; Fourier basis ; minimax ; nonparanetric regression ; Wavelets

Date: 2003-02-27

Prépublication numéro: PMA-799

Front pages