Sparse estimation for functional semiparametric additive models

We propose a functional semiparametric additive model for the effects of a functional covariate and several scalar covariates and a scalar response. The effect of the functional covariate is modeled nonparametrically, while a linear form is adopted to model the effects of the scalar covariates. This strategy can enhance flexibility in modeling the effect of the functional covariate and maintain interpretability for the effects of scalar covariates simultaneously. We develop the method for estimating the functional semiparametric additive model by smoothing and selecting non-vanishing components for the functional covariate. Asymptotic properties of our method are also established. Two simulation studies are implemented to compare our method with various conventional methods. We demonstrate our method with two real applications.