Spline Estimator for the Functional Linear Regression with Functional Response

The article is devoted to a regression setting where both, the response and the predictor, are random functions defined on some compact sets of R. We consider functional linear (auto)regression and we face the estimation of a bivariate functional parameter. Conditions for existence and uniqueness of the parameter are given and an estimator based on a B-splines expansion is proposed using the penalized least squares method. A simulation study is provided to illustrate performance of the estimator. Some convergence results concerning the error of prediction are given as well.