Profile likelihood inferences on semiparametric varying-coefficient partially linear models

Jianqing Fan, Tao Huang

Research output: Contribution to journalArticlepeer-review

554 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)1031-1057
Number of pages27
Issue number6
StatePublished - Dec 2005
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistics and Probability


  • Generalized likelihood ratio statistics
  • Local linear regression
  • Partially linear models
  • Profile likelihood
  • Varying-coefficient partially linear models
  • Wald statistics


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