Fitting a Bivariate Additive Model by Local Polynomial Regression

While the additive model is a popular nonparametric regression method, many of its theoretical properties are not well understood, especially when the backfitting algorithm is used for computation of the the estimators. This article explores those properties when the additive model is fitted by local polynomial regression. Sufficient conditions guaranteeing the asymptotic existence of unique estimators for the bivariate additive model are given. Asymptotic approximations to the bias and the variance of a homoskedastic bivariate additive model with local polynomial terms are computed. This model is shown to have the same rate of convergence as that of univariate local polynomial regression. We also investigate the estimation of derivatives of the additive component functions