A New Functional Estimation Procedure for Varying Coefficient Models

Abstract

There has been substantial research interest in developing various estimation procedures for varying coefficient models. Most methods in the literature require specifying a working covariance structure. In case of a misspecified structure, estimation of the varying coefficient function may be deficient. Taking advantage of functional principal component analysis, we propose a new functional estimation procedure for varying coefficient models which does not need a working covariance structure. Weak convergence property for the proposed estimators has been established. Based on the simulation studies, the proposed procedure works better than the naive local linear regression with working independence error structure by Zhu et al. and Cholesky decomposition method by Lin et al. We apply our method to analyze the growth data of newborn infants in a real medical study and produce interpretable results.