Asymptotically efficient estimators of the drift function in ergodic diffusion processes

Jean-Yves Brua (1)

1 IRMA - Institut de Recherche Mathématique Avancée

This paper deals with the pointwise estimation of the drift function of an ergodic diffusion using the absolute error loss. The optimal convergence rate and the sharp asymptotic lower bound are found for the minimax risk. An asymptotically effcient kernel estimator is constructed.

Mots clés: Asymptotic efficiency; Drift; Ergodic diffusion; Minimax; Nonparametric estimation

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Jean-Yves Brua. Asymptotically efficient estimators of the drift function in ergodic diffusion processes. 2008. ⟨hal-00437558⟩