Regularized functional regression modeling for functional response and predictors

Abstract

We consider the problem of constructing a functional regression modeling with functional predictors and a functional response. Discretely observed data for each individual are expressed as a smooth function, using Gaussian basis functions. The functional regression model is estimated by the maximum penalized likelihood method, assuming that the coefficient parameters are transformed into a functional form. A crucial issue in constructing functional regression models is the selection of regularization parameters involved in the regularization method. We derive informationtheoretic and Bayesian model selection criteria for evaluating the estimated model. Monte Carlo simulations and real data analysis are conducted to examine the performance of our functional regression modeling strategy.