Adaptive sequential estimation for ergodic diffusion processes in quadratic metric. Part 2: Asymptotic efficiency.

Leonid Galtchouk (1) , Serguey Pergamenshchikov (2)

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

Asymptotic efficiency is proved for the constructed in part 1 procedure, i.e. Pinsker's constant is found in the asymptotic lower bound for the minimax quadratic risk. It is shown that the asymptotic minimax quadratic risk of the constructed procedure coincides with this constant.

Mots clés: Adaptive estimation; asymptotic bounds; efficient estimation; nonparametric estimation; Pinsker's constant.; Pinsker's constant

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

Leonid Galtchouk, Serguey Pergamenshchikov. Adaptive sequential estimation for ergodic diffusion processes in quadratic metric. Part 2: Asymptotic efficiency.. 2008. ⟨hal-00269313⟩