Adaptive smoothing spline estimator for the function-on-function linear regression model

Abstract In this paper, we propose an adaptive smoothing spline (AdaSS) estimator for the function-on-function linear regression model where each value of response, at any domain point, depends on full trajectory predictor. The AdaSS is obtained by optimization objective function with two spatially penalties, based initial estimates partial derivatives coefficient function. This allows proposed to adapt more easily true over regions large curvature and not be undersmoothed remaining part domain. A novel evolutionary algorithm developed ad hoc obtain tuning parameters. Extensive Monte Carlo simulations have been carried out compare competitors that already appeared in literature before. results show our proposal mostly outperforms competitor terms estimation prediction accuracy. Lastly, those advantages are illustrated also real-data benchmark examples. implemented package , openly available online CRAN.