Profile likelihood inferences on semiparametric varying-coefficient partially linear models

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…

• NS
  National Science Foundation

  Awards: 0355179, DMS-0354223, DMS-0355179, 0354223
• CU
  Chinese University of Hong Kong
• NI
  National Institutes of Health

  Award: R01 HL69720