Efficient adaptive nonparametric estimation in heteroscedastic regression models

Leonid Galtchouk (1) , Sergei Pergamenshchikov

1 IRMA - Institut de Recherche Mathématique Avancée

An adaptive nonparametric estimation procedure is constructed for heteroscedastic regression. A non-asymptotic upper bound for the quadratic risk (the oracle inequality) is obtained. Asymptotic efficiency of this procedure is proved, i.e. Pinsker's constant is found in the asymptotical lower bound for the risk. It is shown that the asymptotical quadratic risk for the constructed procedure coincides with this constant.

Mots clés: adaptive estimation; Pinsker's constant; "adaptive estimation; asymptotic bounds; efficient estimation; heteroscedastic regression; nonparametric estimation; non-asymptotic bounds; oracle inequality; Pinsker's constant"

Domaines: Statistiques [math.ST]

Leonid Galtchouk, Sergei Pergamenshchikov. Efficient adaptive nonparametric estimation in heteroscedastic regression models. 2005. ⟨hal-00129707⟩