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

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

Adaptive estimation for inverse problems : a logarithmic effect in $L_2$

Auteur(s):

Code(s) de Classification MSC:

Résumé: This note presents a method of adaptive estimation for a class of inverse problems with random noise. We show that the proposed method attains the best rate of adaptive estimation in $L_2$, but this rate is slower than the "non-adaptive" minimax rate by a logarithmic factor.

Mots Clés: Adaptive curve estimation ; Statistical inverse problems ; Heavily ill-posed problems ; Optimal rate of adaptation

Date: 2000-03-27

Prépublication numéro: PMA-579

Postscript file : PMA-579.ps