The Annals of Statistics

Smooth backfitting in generalized additive models

Kyusang Yu, Byeong U. Park, and Enno Mammen

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Abstract

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

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

Dates
First available in Project Euclid: 1 February 2008

Permanent link to this document
https://projecteuclid.org/euclid.aos/1201877300

Digital Object Identifier
doi:10.1214/009053607000000596

Mathematical Reviews number (MathSciNet)
MR2387970

Zentralblatt MATH identifier
1132.62028

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

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

Citation

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. https://projecteuclid.org/euclid.aos/1201877300


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