Adaptive asymptotically efficient estimation in heteroscedastic nonparametric regression

Leonid Galtchouk (1) , Serguei Pergamenchtchikov (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 an unknown nonparametric regression. %\cite{GaPe1}. 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 estimates

Mots clés: asymptotic bounds; adaptive estimation; efficient estimation; heteroscedastic regression; nonparametric regression; Pinsker's constant

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

Leonid Galtchouk, Serguei Pergamenchtchikov. Adaptive asymptotically efficient estimation in heteroscedastic nonparametric regression. Journal of the Korean Statistical Society, 2008, 38 (4), pp.305-322. ⟨hal-00454081⟩