Asymptotic distribution of robust k-nearest neighbour estimator for functional nonparametric models

Mohammed Kadi Attouch, Tawfik Benchikh

We propose a family of robust nonparametric estimators for robust regression function based on k-nearest neighbour (k-NN) method. We establish the asymptotic normality of the estimator under the concentration properties on small balls of the probability measure of the functional explanatory variables.