Functional singular component analysis based functional additive models

Abstract

We propose a method which uses functional singular component to establish functional additive models. The proposed methodology reduces the curve regression problem to ordinary (i.e., scalar) additive regression problems of the singular components of the predictor process and response process. Consistency of estimators for the nonparametric function and prediction are proved, respectively. A simulation study is conducted to investigate the finite sample performances of the proposed estimators.