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Yu, Kyusang; Park, Byeong U.; Mammen, Enno

Smooth backfitting in generalized additive models. (English) Zbl 1132.62028

Ann. Stat. 36, No. 1, 228-260 (2008).
Summary: 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 two-stage estimator proposed by J. L. Horowitz and E. Mammen [Ann. Stat. 32, No. 6, 2412–2443 (2004; Zbl 1069.62035)] is also made.

Cited in 53 Documents

MSC:

62G08 Nonparametric regression and quantile regression
62G20 Asymptotic properties of nonparametric inference
65C60 Computational problems in statistics (MSC2010)
62G07 Density estimation
65R20 Numerical methods for integral equations

Keywords:

generalized additive models; smoothed likelihood; smooth backfitting; curse of dimensionality; Newton-Kantorovich theorem

Citations:

Zbl 1069.62035
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Full Text: DOI arXiv Euclid

References:

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