Adaptive sequential estimation for ergodic diffusion processes in quadratic metric. Part 1: Sharp non-asymptotic oracle inequalities.

Leonid Galtchouk (1) , Sergey Pergamenshchikov (2)

1 IRMA - Institut de Recherche Mathématique Avancée
2 LMRS - Laboratoire de Mathématiques Raphaël Salem

An adaptive nonparametric estimation procedure is constructed for the estimation problem of the drift coefficient in diffusion processes. A non-asymptotic oracle upper bound for the integral quadratic risk is obtained.

Mots clés: Adaptive estimation; asymptotic bounds; efficient estimation; nonparametric estimation; non-asymptotic estimation; oracle inequality; Pinsker's constant

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

Leonid Galtchouk, Sergey Pergamenshchikov. Adaptive sequential estimation for ergodic diffusion processes in quadratic metric. Part 1: Sharp non-asymptotic oracle inequalities.. 2007. ⟨hal-00177875⟩