Estimation of Hilbertian varying coefficient models

In this paper we discuss the estimation of a fairly general type of varying coefficient model. The model is for a re-sponse variable that takes values in a general Hilbert space and allows for various types of additive interaction terms in representing the effects of predictors. It also accommo-dates both continuous and discrete predictors. We develop a powerful technique of estimating the very general model. Our approach may be used in a variety of situations where one needs to analyze the relation between a set of predic-tors and a Hilbertian response. We prove the existence of the estimators of the model itself and of its components, and also the convergence of a backfitting algorithm that re-alizes the estimators. We derive the rates of convergence of the estimators and their asymptotic distributions. We also demonstrate via simulation study that our approach works efficiently, and illustrate its usefulness through a real data application.