title: Structured functional additive regression in reproducing kernel Hilbert spaces.
abstract: Functional additive models (FAMs) provide a flexible yet simple framework for regressions involving functional predictors. The utilization of data-driven basis in an additive rather than linear structure naturally extends the classical functional linear model. However, the critical issue of selecting nonlinear additive components has been less studied. In this work, we propose a new regularization framework for the structure estimation in the context of Reproducing Kernel Hilbert Spaces. The proposed approach takes advantage of the functional principal components which greatly facilitates the implementation and the theoretical analysis. The selection and estimation are achieved by penalized least squares using a penalty which encourages the sparse structure of the additive components. Theoretical properties such as the rate of convergence are investigated. The empirical performance is demonstrated through simulation studies and a real data application.
authors.affiliation: Virginia Tech, Blacksburg, USA.
authors.forename: Hongxiao
authors.initials: H
authors.lastname: Zhu
authors.affiliation: University of Toronto, Toronto, Canada.
authors.forename: Fang
authors.initials: F
authors.lastname: Yao
authors.affiliation: University of Arizona, Tucson, USA.
authors.forename: Hao Helen
authors.initials: HH
authors.lastname: Zhang
keywords: Additive models; Component selection; Functional data analysis; Principal components; Reproducing kernel Hilbert space; Smoothing spline