Open Access
February 1997 Fitting a bivariate additive model by local polynomial regression
Jean D. Opsomer, David Ruppert
Ann. Statist. 25(1): 186-211 (February 1997). DOI: 10.1214/aos/1034276626

Abstract

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.

Citation

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Jean D. Opsomer. David Ruppert. "Fitting a bivariate additive model by local polynomial regression." Ann. Statist. 25 (1) 186 - 211, February 1997. https://doi.org/10.1214/aos/1034276626

Information

Published: February 1997
First available in Project Euclid: 10 October 2002

zbMATH: 0869.62026
MathSciNet: MR1429922
Digital Object Identifier: 10.1214/aos/1034276626

Subjects:
Primary: 62G07
Secondary: 62H99

Keywords: Additive model , backfitting , existence , local polynomial regression , Optimal rates

Rights: Copyright © 1997 Institute of Mathematical Statistics

Vol.25 • No. 1 • February 1997
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