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

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

Exact constants for pointwise adaptive estimation under the Riesz transform

Auteur(s):

Code(s) de Classification MSC:

Résumé: We consider nonparametric estimation of a multivariate function and its partial derivatives at a fixed point when the Riesz transform of the function is observed in Gaussian white noise. We assume that the unknown function belongs to some Sobolev class and construct an estimation procedure which achieves the best asymptotic minimax risk when the smoothness of the function is unknown.

Mots Clés: Adaptive curve estimation ; Bandwidth selection ; Deconvolution ; Exact constants in nonparametric smoothing ; Gaussian white noise ; Inverse problems ; Kernel estimation ; Minimax risk

Date: 2001-11-15

Prépublication numéro: PMA-699