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

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

Bayesian maximum likelihood and semiparametric second order efficiency

Auteur(s):

Code(s) de Classification MSC:

Résumé: We consider the problem of estimation of a shift parameter of an unknown symmetric function in Gaussian white noise. We introduce a notion of semiparametric second order efficiency and propose estimators that are semiparamerically efficient and second order efficient in our model. The estimators are based on the idea of Bayesian maximum likelihood. We argue that second order efficiency is crucial in semiparametric problems since only the second order terms in asymptotic expansion for the risk account for the behavior of the ``nonparametric component" of a semiparametric procedure, and they are not dramatically smaller than the first order terms.

Mots Clés: semiparametric estimation ; estimating a shift of a nonparametric function ; second order efficiency ; Bayesian maximum likelihood, exact minimax asymptotics

Date: 2003-09-09

Prépublication numéro: PMA-842