| Université Paris 6 Pierre et Marie Curie | Université Paris 7 Denis Diderot | |
| CNRS U.M.R. 7599 | ||
| ``Probabilités et Modèles Aléatoires'' | ||
Auteur(s):
Code(s) de Classification MSC:
Résumé: The subject of this paper is to estimate adaptively the common probability density of $n$ independent, identically distributed random variables. The estimation is done at a fixed point $x_{0}\in I\!\!R$, over the density functions that belong to the Sobolev class $W_n(\beta ,L)$. We consider the adaptive problem setup, where the regularity parameter $\beta $ is unknown and varies in a given set $B_{n}$. A sharp adaptive estimator is obtained, and the explicit asymptotical constant, associated to its rate of convergence is found.
Mots Clés: Density estimation ; exact asymptotics ; pointwise risk ; sharp adaptive estimator
Date: 2000-11-16
Prépublication numéro: PMA-621