Sharp non-asymptotic oracle inequalities for nonparametric heteroscedastic regression models

Leonid Galtchouk (1) , Serguei Pergamenchtchikov (2)

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

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

Mots clés: Adaptive estimation; Heteroscedastic regression; Nonasymptotic estimation; Nonparametric estimation; Oracle inequality

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

Leonid Galtchouk, Serguei Pergamenchtchikov. Sharp non-asymptotic oracle inequalities for nonparametric heteroscedastic regression models. Journal of Nonparametric Statistics, 2009, 21 (1), pp.1-16. ⟨hal-00454079⟩