The Annals of Statistics

Fitting a bivariate additive model by local polynomial regression

Jean D. Opsomer and David Ruppert

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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.

Article information

Ann. Statist., Volume 25, Number 1 (1997), 186-211.

First available in Project Euclid: 10 October 2002

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62G07: Density estimation
Secondary: 62H99: None of the above, but in this section

Additive model local polynomial regression optimal rates existence backfitting


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.

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