Adaptive estimators for nonparametric heteroscedastic regression models

This paper deals with the estimation of a regression function at a fixed point in nonparametric heteroscedastic regression models with Gaussian noise. We assume that the variance of the noise depends on the regressor and on the regression function. We make use of the minimax absolute error risk taken over a Holder class of regression functions. As the smoothness of the regression function is supposed to be unknown, we construct an adaptive kernel estimator which attains the minimax rate. More precisely, we give an asymptotic upper bound and an asymptotic lower bound for the minimax risk.