Asymptotic Distribution of Robust Estimator for Functional Nonparametric Models

We propose a family of robust nonparametric estimators for regression function based on kernel 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. Useful applications to prediction, discrimination in a semi-metric space, and confidence curves are given. In addition, to highlight the generality of our purpose and to emphasize the role of each of our hypotheses, several special cases of our general conditions are also discussed. Finally, some numerical study in chemiometrical real data are carried out to compare the sensitivity to outliers between the classical and robust regression.