Recursive nonparametric regression estimation for independent functional data
Résumé
We propose an automatic selection of the bandwidth of the recursive nonparametric estimation of the regression function defined by the stochastic approximation algorithm. Here the explanatory data are curves and the response is real. We compare our recursive estimators with the nonrecursive estimator proposed by Ferraty and Vieu (2002). The two methods are based on the wild bootstrapping approach, where resampling is done from a suitably estimated residual distribution. Moreover, we establish a central limit theorem for our proposed recursive estimators. We use the wild bootstrap to select the bandwidth and some special stepsizes. As such, the proposed recursive estimators are competitive in terms of the estimation error, but much better in terms of computational costs. The proposed estimators are used in simulated and real functional data sets.