Varying-Coefficient Additive Models for Functional Data

Abstract Both varying-coefficient and additive models have been studied extensively in the literature as extensions to linear models. They have also been extended to functional response data. However, existing extensions are still not sufficiently flexible to reflect the functional feature of the responses. In this paper, we extend both varying-coefficient and additive models to a much more flexible “varying-coefficient additive model” and propose a simple algorithm to estimate the nonparametric additive and varying-coefficient components of this model. We establish the L2 rate of convergence for each component function and demonstrate the applicability of the new model through traffic data.