Adaptive asymptotically efficient estimation in heteroscedastic nonparametric regression via model selection.

Leonid Galtchouk (1) , Serguey Pergamenshchikov (2)

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

The paper deals with asymptotic properties of the adaptive procedure proposed in the author paper, 2007, for estimating a unknown nonparametric regression. We prove that this procedure is asymptotically efficient for a quadratic risk, i.e. the asymptotic quadratic risk for this procedure coincides with the Pinsker constant which gives a sharp lower bound for the quadratic risk over all possible estimators.

Mots clés: asymptotic bounds; adaptive estimation; efficient estimation; heteroscedastic regression; nonparametrique regression; Pinsker constant

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

Leonid Galtchouk, Serguey Pergamenshchikov. Adaptive asymptotically efficient estimation in heteroscedastic nonparametric regression via model selection.. 2008. ⟨hal-00326910⟩