Adaptive nonparametric estimation in heteroscedastic regression models. Part 1: Sharp non-asymptotic Oracle inequalities.

Leonid Galtchouk (1) , Serguey Pergamenshchikov (2)

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

An adaptive nonparametric estimation procedure is constructed for the estimation problem of heteroscedastic regression when the noise variance depends on the unknown regression. A non-asymptotic upper bound for a quadratic risk (an oracle inequality) is constructed.

Mots clés: oracle inequality; adaptive estimation; heteroscedastic regression; non-asymptotic estimation; nonparametric estimation; oracle inequality.

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

Leonid Galtchouk, Serguey Pergamenshchikov. Adaptive nonparametric estimation in heteroscedastic regression models. Part 1: Sharp non-asymptotic Oracle inequalities.. Journal of Nonparametric Statistics, 2009, 21 (1), pp.1-16. ⟨10.1080/10485250802504096⟩. ⟨hal-00269196⟩