Asymptotically efficient estimators for nonparametric heteroscedastic regression models

Jean-Yves Brua (1)

1 IRMA - Institut de Recherche Mathématique Avancée

This paper concerns the estimation of the regression function at a given point in nonparametric heteroscedastic models with Gaussian noise or with noise having unknown distribution. In the two cases an asymptotically efficient kernel estimator is constructed for the minimax absolute error risk.

Mots clés: Asymptotical efficiency; kernel estimator; minimax; nonparametric regression

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

Jean-Yves Brua. Asymptotically efficient estimators for nonparametric heteroscedastic regression models. Statistical Methodology, 2009, 6 (1), pp.47-60. ⟨10.1016/j.stamet.2008.02.009⟩. ⟨hal-00178536v2⟩