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

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

Sharp adaptation for inverse problems with random noise

Auteur(s):

Code(s) de Classification MSC:

Résumé: We consider a heteroscedastic sequence space setup with polynomially increasing variances of observations that allows to treat a number of inverse problems, in particular multivariate ones. We propose an adaptive estimator that attains simultaneously exact asymptotic minimax constants on every ellipsoid of functions within a wide scale (that includes ellipoids with polynomially and exponentially decreasing axes) and, at the same time, satisfies asymptotically exact oracle inequalities within any class of linear estimates having monotone non-decreasing weights. As application, we construct sharp adaptive estimators in the problems of deconvolution and tomography.

Mots Clés: Adaptive curve estimation ; Statistical inverse problems ; Exact minimax constants ; Tomography ; Deconvolution

Date: 2000-01-17

Prépublication numéro: PMA-559

Postscript file : PMA-559.ps