Abstract
It is well known that the nonparametric estimation of the regression function is highly sensitive to the presence of even a small proportion of outliers in the data. To solve the problem of typical observations when the covariates of the nonparametric component are functional, the robust estimates for the regression parameter and regression operator are introduced. The main propose of the paper is to consider data-driven methods of selecting the number of neighbors in order to make the proposed processes fully automatic. We use the k Nearest Neighbors procedure (kNN) to construct the kernel estimator of the proposed robust model. Under some regularity conditions, we state consistency results for kNN functional estimators, which are uniform in the number of neighbors (UINN). Furthermore, a simulation study and an empirical application to a real data analysis of octane gasoline predictions are carried out to illustrate the higher predictive performances and the usefulness of the kNN approach.