Adaptive nonparametric estimation in heteroscedastic regression models. Part 2: Asymptotic efficiency.

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 estimation of unknown nonparametric regression. We prove that this procedure is asymptotically efficient for a quadratic risk. It means that the asymptotic quadratic risk for this procedure coincides with a sharp lower bound.

Mots clés: nonparametric estimation; Adaptive estimation; asymptotic bounds; efficient estimation; heteroscedastic; nonparametric estimation.

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

Leonid Galtchouk, Serguey Pergamenshchikov. Adaptive nonparametric estimation in heteroscedastic regression models. Part 2: Asymptotic efficiency.. Journal of the Korean Statistical Society, 2009, 35 p. ⟨10.1016/j.jkss.2008.12.001⟩. ⟨hal-00269303⟩