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dec 2005 Profile likelihood inferences on semiparametric varying-coefficient partially linear models
Jianqing Fan, Tao Huang
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Bernoulli 11(6): 1031-1057 (dec 2005). DOI: 10.3150/bj/1137421639


Varying-coefficient partially linear models are frequently used in statistical modelling, but their estimation and inference have not been systematically studied. This paper proposes a profile least-squares technique for estimating the parametric component and studies the asymptotic normality of the profile least-squares estimator. The main focus is the examination of whether the generalized likelihood technique developed by Fan et al. is applicable to the testing problem for the parametric component of semiparametric models. We introduce the profile likelihood ratio test and demonstrate that it follows an asymptotically χ2 distribution under the null hypothesis. This not only unveils a new Wilks type of phenomenon, but also provides a simple and useful method for semiparametric inferences. In addition, the Wald statistic for semiparametric models is introduced and demonstrated to possess a sampling property similar to the profile likelihood ratio statistic. A new and simple bandwidth selection technique is proposed for semiparametric inferences on partially linear models and numerical examples are presented to illustrate the proposed methods.


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Jianqing Fan. Tao Huang. "Profile likelihood inferences on semiparametric varying-coefficient partially linear models." Bernoulli 11 (6) 1031 - 1057, dec 2005.


Published: dec 2005
First available in Project Euclid: 16 January 2006

zbMATH: 1098.62077
MathSciNet: MR2189080
Digital Object Identifier: 10.3150/bj/1137421639

Keywords: generalized likelihood ratio statistics , local linear regression , partially linear models , profile likelihood , varying-coefficient partially linear models , Wald statistics

Rights: Copyright © 2005 Bernoulli Society for Mathematical Statistics and Probability


Vol.11 • No. 6 • dec 2005
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