The Annals of Statistics
- Ann. Statist.
- Volume 25, Number 1 (1997), 186-211.
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 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 homoscedastic bivariate additive model with local polynomial terms of odd and even degree are computed. This model is shown to have the same rate of convergence as that of univariate local polynomial regression.
Ann. Statist., Volume 25, Number 1 (1997), 186-211.
First available in Project Euclid: 10 October 2002
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Opsomer, Jean D.; Ruppert, David. Fitting a bivariate additive model by local polynomial regression. Ann. Statist. 25 (1997), no. 1, 186--211. doi:10.1214/aos/1034276626. https://projecteuclid.org/euclid.aos/1034276626