Smooth backfitting for errors-in-variables varying coefficient regression models

Abstract

Varying coefficient models inherit the simplicity and easy interpretation of classical linear models while enjoying the flexibility of nonparametric models. They are very useful in analyzing the relation between a response and a set of predictors. There has been no study, however, on the estimation of varying coefficients when the predictors, on which the varying coefficients depend, are contaminated by measurement errors. A new kernel smoothing technique that is tailored to the structure of an underlying varying coefficient model as well as corrects for the bias due to the measurement errors is developed here. The estimators of the varying coefficients are given implicitly by solving a system of integral equations, whose implementation requires an iterative backfitting procedure. The existence of a unique solution and the convergence of the associated backfitting algorithm are established theoretically. Some numerical evidences that support the theory and demonstrate the success of the proposed methodology are presented.