| 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: There are a lot of asymptotically first-order efficient estimators in the problem of invariant density estimation of ergodic diffusion process. We consider the problem of asymptotically second-order efficient nonparametric estimation of this density, i.e., we have two problems. The first one is to introduce a second-order lower bound on the risks of all estimators and the second is to construct an estimator which attains this bound. We realize this program (bound+estimator) following the Pinsker's approach.
Mots Clés: ergodic diffusion ; invariant density ; second order efficiency ;
nonparametric estimation ; Pinsker bound
Date: 2003-02-26
Prépublication numéro: PMA-797