2011
DOI: 10.3150/10-bej296
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Semi-parametric regression: Efficiency gains from modeling the nonparametric part

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 t… Show more

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Cited by 28 publications
(19 citation statements)
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References 25 publications
(41 reference statements)
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“…A rigorous proof of Theorem 1 can be done as in Yu et al (2009) by using Halperin's Theorem for iterative alternating projections and Proposition A.3.5 in Bickel, Klaassen, Ritov, and Wellner (1993). The information bound (8) can be decomposed as…”
Section: Semiparametric Efficiencymentioning
confidence: 99%
See 4 more Smart Citations
“…A rigorous proof of Theorem 1 can be done as in Yu et al (2009) by using Halperin's Theorem for iterative alternating projections and Proposition A.3.5 in Bickel, Klaassen, Ritov, and Wellner (1993). The information bound (8) can be decomposed as…”
Section: Semiparametric Efficiencymentioning
confidence: 99%
“…We will take an approach similar to Yu et al (2009) and present a heuristic argument here. The rigorous proof can be done as in Yu et al (2009).…”
Section: Semiparametric Efficiencymentioning
confidence: 99%
See 3 more Smart Citations