Smooth backfitting in generalized additive models
Kyusang Yu, Byeong U. Park, and Enno Mammen
Source: Ann. Statist. Volume 36, Number 1 (2008), 228-260.
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.
Primary Subjects: 62G07
Secondary Subjects: 62G20
Keywords: Generalized additive models; smoothed likelihood; smooth backfitting; curse of dimensionality; Newton–Kantorovich theorem
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Permanent link to this document: http://projecteuclid.org/euclid.aos/1201877300
Digital Object Identifier: doi:10.1214/009053607000000596
Mathematical Reviews number (MathSciNet):
MR2387970
Zentralblatt MATH identifier:
1132.62028
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