Abstract
In this paper, we propose a family of robust nonparametric estimators for a regression function with unknown scale parameter based on the kernel method. We establish the asymptotic normality of the estimators for functional explanatory variables when the observations exhibit some kind of dependence (stationary ergodic process). This approach can be used for predicting and for building confidence regions. A simulation study is conducted to support our theoretical results and to exhibit the good behavior of the proposed estimator for finite samples with different rates of dependency, and particularly in the presence of several outliers in the data set. In addition, a real data study is provided to illustrate the good behavior of our estimator.