Open Access
May 2011 Semi-parametric regression: Efficiency gains from modeling the nonparametric part
Kyusang Yu, Enno Mammen, Byeong U. Park
Bernoulli 17(2): 736-748 (May 2011). DOI: 10.3150/10-BEJ296


It is widely admitted that structured nonparametric modeling that circumvents the curse of dimensionality is important in nonparametric estimation. In this paper we show that the same holds for semi-parametric estimation. We argue that estimation of the parametric component of a semi-parametric model can be improved essentially when more structure is put into the nonparametric part of the model. We illustrate this for the partially linear model, and investigate efficiency gains when the nonparametric part of the model has an additive structure. We present the semi-parametric Fisher information bound for estimating the parametric part of the partially linear additive model and provide semi-parametric efficient estimators for which we use a smooth backfitting technique to deal with the additive nonparametric part. We also present the finite sample performances of the proposed estimators and analyze Boston housing data as an illustration.


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Kyusang Yu. Enno Mammen. Byeong U. Park. "Semi-parametric regression: Efficiency gains from modeling the nonparametric part." Bernoulli 17 (2) 736 - 748, May 2011.


Published: May 2011
First available in Project Euclid: 5 April 2011

zbMATH: 1345.62046
MathSciNet: MR2787613
Digital Object Identifier: 10.3150/10-BEJ296

Keywords: partially linear additive models , Profile estimator , semi-parametric efficiency , smooth backfitting

Rights: Copyright © 2011 Bernoulli Society for Mathematical Statistics and Probability

Vol.17 • No. 2 • May 2011
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