Statistical inference on semi-parametric partial linear additive models

Chuan hua Wei, Chunling Liu

Research output: Journal article publicationJournal articleAcademic researchpeer-review

10 Citations (Scopus)

Abstract

In the framework of partial linear additive models, we first develop a profile least-squares estimation of the parametric component based on Liang et al.'s [(2008), 'Additive Partial Linear Models with Measurement Errors', Biometrika, 95(3), 667-678] work. This estimator is shown to be asymptotically normal and root-n consistent without requirement of undersmoothing of the nonparametric component. Next, when some additional linear restrictions on the parametric component are available, we postulate a restricted profile least-squares estimator for the parametric component and prove the asymptotic normality of the resulting estimator. To check the validity of the linear constraints on the parametric component, we explore a generalised likelihood ratio test statistic and demonstrate that it follows asymptotically chi-squared distribution under the null hypothesis. Thus, the result unveils a new Wilks type of phenomenon. Simulation studies are conducted to illustrate the proposed methods. An application to the crime rate data in Columbus (Ohio) has been carried out.
Original languageEnglish
Pages (from-to)809-823
Number of pages15
JournalJournal of Nonparametric Statistics
Volume24
Issue number4
DOIs
Publication statusPublished - 1 Dec 2012

Keywords

  • backfitting
  • generalised likelihood ratio test
  • partial linear additive models
  • profile least-squares
  • restricted estimation

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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