The Annals of Statistics

Smooth backfitting in generalized additive models

Kyusang Yu, Byeong U. Park, and Enno Mammen

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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.

Article information

Ann. Statist., Volume 36, Number 1 (2008), 228-260.

First available in Project Euclid: 1 February 2008

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62G07: Density estimation
Secondary: 62G20: Asymptotic properties

Generalized additive models smoothed likelihood smooth backfitting curse of dimensionality Newton–Kantorovich theorem


Yu, Kyusang; Park, Byeong U.; Mammen, Enno. Smooth backfitting in generalized additive models. Ann. Statist. 36 (2008), no. 1, 228--260. doi:10.1214/009053607000000596.

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