Robust Regression for Functional Time Series Data

Abstract

We propose a family of robust nonparametric estimators for regression function based on the kernel method. We establish the almost complete convergence rate of these estimators under the α-mixing assumption and on the concentration properties on small balls of the probability measure of the functional regressors. Some applications to physics real data have been made. These results are extensions to dependent data of the results given by Azzedine et al. (2008).