Nonparametric regression estimation for functional random design
Résumé
This work deals with the study of the estimation of the functional regression operator when the explanatory variable takes its values in some abstract space of functions. The main goal is to establish the exact rate of convergence of the mean squared error of the functional version of the Nadaraya-Watson kernel estimator when the errors come from a stationary process under long or short memory and based on random functional data. Moreover, these theoretical results are checked through some simulations with regular (smooth) and irregular curves and then with real data.