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Profile likelihood inferences on semiparametric varying-coefficient partially linear models

Jianqing Fan Tao Huang

Statistics Theory and Methods mathscidoc:1912.43257

Bernoulli, 11, (6), 1031-1057, 2005
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 2 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
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@inproceedings{jianqing2005profile,
  title={Profile likelihood inferences on semiparametric varying-coefficient partially linear models},
  author={Jianqing Fan, and Tao Huang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221113319707948817},
  booktitle={Bernoulli},
  volume={11},
  number={6},
  pages={1031-1057},
  year={2005},
}
Jianqing Fan, and Tao Huang. Profile likelihood inferences on semiparametric varying-coefficient partially linear models. 2005. Vol. 11. In Bernoulli. pp.1031-1057. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221113319707948817.
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