Empirical likelihood inference in partially linear single-index models for longitudinal data

Gaorong Li, Lixing Zhu*, Liugen Xue, Sanying Feng

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

41 Citations (Scopus)


The empirical likelihood method is especially useful for constructing confidence intervals or regions of parameters of interest. Yet, the technique cannot be directly applied to partially linear single-index models for longitudinal data due to the within-subject correlation. In this paper, a bias-corrected block empirical likelihood (BCBEL) method is suggested to study the models by accounting for the within-subject correlation. BCBEL shares some desired features: unlike any normal approximation based method for confidence region, the estimation of parameters with the iterative algorithm is avoided and a consistent estimator of the asymptotic covariance matrix is not needed. Because of bias correction, the BCBEL ratio is asymptotically chi-squared, and hence it can be directly used to construct confidence regions of the parameters without any extra Monte Carlo approximation that is needed when bias correction is not applied. The proposed method can naturally be applied to deal with pure single-index models and partially linear models for longitudinal data. Some simulation studies are carried out and an example in epidemiology is given for illustration.

Original languageEnglish
Pages (from-to)718-732
Number of pages15
JournalJournal of Multivariate Analysis
Issue number3
Publication statusPublished - Mar 2010

Scopus Subject Areas

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

User-Defined Keywords

  • Longitudinal data
  • Partially linear single-index model
  • Empirical likelihood
  • Confidence
  • region
  • Bias correction


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