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

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

On second order asymptotically efficient estimation of invariant density for ergodic diffusion

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