Open Access
February 2008 Smooth backfitting in generalized additive models
Kyusang Yu, Byeong U. Park, Enno Mammen
Ann. Statist. 36(1): 228-260 (February 2008). DOI: 10.1214/009053607000000596


Generalized additive models have been popular among statisticians and data analysts in multivariate nonparametric regression with non-Gaussian responses including binary and count data. In this paper, a new likelihood approach for fitting generalized additive models is proposed. It aims to maximize a smoothed likelihood. The additive functions are estimated by solving a system of nonlinear integral equations. An iterative algorithm based on smooth backfitting is developed from the Newton–Kantorovich theorem. Asymptotic properties of the estimator and convergence of the algorithm are discussed. It is shown that our proposal based on local linear fit achieves the same bias and variance as the oracle estimator that uses knowledge of the other components. Numerical comparison with the recently proposed two-stage estimator [Ann. Statist. 32 (2004) 2412–2443] is also made.


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Kyusang Yu. Byeong U. Park. Enno Mammen. "Smooth backfitting in generalized additive models." Ann. Statist. 36 (1) 228 - 260, February 2008.


Published: February 2008
First available in Project Euclid: 1 February 2008

zbMATH: 1132.62028
MathSciNet: MR2387970
Digital Object Identifier: 10.1214/009053607000000596

Primary: 62G07
Secondary: 62G20

Keywords: curse of dimensionality , generalized additive models , Newton–Kantorovich theorem , smooth backfitting , smoothed likelihood

Rights: Copyright © 2008 Institute of Mathematical Statistics

Vol.36 • No. 1 • February 2008
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