Empirical likelihood for a varying coefficient partially linear model with diverging number of parameters

Gaorong Li, Lu Lin, Lixing ZHU*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

49 Citations (Scopus)

Abstract

The purpose of this paper is two-fold. First, for the estimation or inference about the parameters of interest in semiparametric models, the commonly used plug-in estimation for infinite-dimensional nuisance parameter creates non-negligible bias, and the least favorable curve or under-smoothing is popularly employed for bias reduction in the literature. To avoid such strong structure assumptions on the models and inconvenience of estimation implementation, for the diverging number of parameters in a varying coefficient partially linear model, we adopt a bias-corrected empirical likelihood (BCEL) in this paper. This method results in the distribution of the empirical likelihood ratio to be asymptotically tractable. It can then be directly applied to construct confidence region for the parameters of interest. Second, different from all existing methods that impose strong conditions to ensure consistency of estimation when diverging the number of the parameters goes to infinity as the sample size goes to infinity, we provide techniques to show that, other than the usual regularity conditions, the consistency holds under moment conditions alone on the covariates and error with a diverging rate being even faster than those in the literature. A simulation study is carried out to assess the performance of the proposed method and to compare it with the profile least squares method. A real dataset is analyzed for illustration.

Original languageEnglish
Pages (from-to)85-111
Number of pages27
JournalJournal of Multivariate Analysis
Volume105
Issue number1
DOIs
Publication statusPublished - Feb 2012

Scopus Subject Areas

  • Statistics and Probability
  • Numerical Analysis
  • Statistics, Probability and Uncertainty

User-Defined Keywords

  • Asymptotic normality
  • Bias correction
  • Curse of dimensionality
  • Empirical likelihood
  • Varying coefficient partially linear model

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