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

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

Sharp adaptive estimation of linear functionals


Code(s) de Classification MSC:

Résumé: We consider estimation of a linear functional $T(f)$ where $f$ is an unknown func- tion observed in Gaussian white noise. We find asymptotically sharp adaptive estimators on various scales of smoothness classes in multidimensional situ- ation. The results allow to evaluate explicitly the effect of dimension (all previous results were one-dimensional) and to treat general scales of classes. Furthermore, we establish a connection between sharp adaptation and mini- max estimation of linear functionals (optimal recovery). Namely, we propose a scheme that reduces the construction of sharp adaptive estimators on a scale of functional classes to a solution of the corresponding optimization problem.

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

Date: 1999-11-17

Prépublication numéro: PMA-540