Smooth backfitting in generalized additive models

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dc.creatorYu, Kyusang
dc.creatorPark, Byeong U.
dc.creatorMammen, Enno
dc.date2008-03-13
dc.date.accessioned2026-07-07T12:17:37Z
dc.date.available2026-07-07T12:17:37Z
dc.descriptionGeneralized 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.
dc.descriptionPublished in at http://dx.doi.org/10.1214/009053607000000596 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)
dc.identifierhttps://arxiv.org/abs/0803.1922
dc.identifierhttp://arxiv.org/abs/0803.1922
dc.identifierAnnals of Statistics 2008, Vol. 36, No. 1, 228-260
dc.identifierdoi:10.1214/009053607000000596
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/212138
dc.subjectStatistics Theory
dc.subject62G07 (Primary) 62G20 (Secondary)
dc.titleSmooth backfitting in generalized additive models
dc.typetext

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