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Smooth backfitting in generalized additive models (2007)
| Citations: | 9 - 6 self |
BibTeX
@MISC{Yu07smoothbackfitting,
author = {Kyusang Yu and Byeong U. Park and Enno Mammen},
title = {Smooth backfitting in generalized additive models},
year = {2007}
}
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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.
Keyphrases
generalized additive model smooth backfitting newton kantorovich theorem numerical comparison nonlinear integral equation additive function smoothed likelihood new likelihood approach multivariate nonparametric regression data analyst two-stage estimator ann local linear fit iterative algorithm asymptotic property oracle estimator non-gaussian response count data
