Bernoulli

  • Bernoulli
  • Volume 17, Number 2 (2011), 736-748.

Semi-parametric regression: Efficiency gains from modeling the nonparametric part

Kyusang Yu, Enno Mammen, and Byeong U. Park

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Abstract

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.

Article information

Source
Bernoulli, Volume 17, Number 2 (2011), 736-748.

Dates
First available in Project Euclid: 5 April 2011

Permanent link to this document
https://projecteuclid.org/euclid.bj/1302009245

Digital Object Identifier
doi:10.3150/10-BEJ296

Mathematical Reviews number (MathSciNet)
MR2787613

Zentralblatt MATH identifier
1345.62046

Keywords
partially linear additive models profile estimator semi-parametric efficiency smooth backfitting

Citation

Yu, Kyusang; Mammen, Enno; Park, Byeong U. Semi-parametric regression: Efficiency gains from modeling the nonparametric part. Bernoulli 17 (2011), no. 2, 736--748. doi:10.3150/10-BEJ296. https://projecteuclid.org/euclid.bj/1302009245


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