Recursive nonparametric regression estimation for dependent strong mixing functional data

摘要

In the present paper, we extend the work of Slaoui (Stat Sin 30:417-437, 2020) in the case of strong mixing data. Since, we are interested in nonparametric regression estimation, we focus on well adapted dependence structures based on mixing type conditions. We study the properties of these regression estimators and compare them with the nonparametric non-recursive regression estimator. The bias, variance and mean squared error are computed explicitly. We showed that using a selected wild bootstrap bandwidth procedure and a special stepsize, our proposed recursive regression estimators allowed us to obtain quite similar results compared to the non-recursive regression estimator under alpha-mixing condition in terms of estimation error and much better in terms of computational costs.