Estimation for partial functional partially linear additive model

A class of scalar-on-function regression estimating the nonparametric effects of a functional predictor and semiparametric effects of multivariate scalar predictors is investigated. The proposed model is motivated by applications considering both functional and scalar predictors with possibly nonlinear effects. A two-step estimation procedure together with functional principal components analysis allows the simultaneous estimation of nonlinear effects of both the functional and scalar predictors. The computation of the proposed estimators is efficient and does not require iterative algorithms, which is desirable for high dimensional setting. Asymptotic properties such as convergence rate and asymptotic normality have been established. Finite sample performances are studied through simulations and data analysis in functional neuroimaging and real estate analytic.