Empirical likelihood confidence regions in a partially linear single-index model

Lixing ZHU*, Liugen Xue

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

195 Citations (Scopus)


Empirical-likelihood-based inference for the parameters in a partially linear single-index model is investigated. Unlike existing empirical likelihood procedures for other simpler models, if there is no bias correction the limit distribution of the empirical likelihood ratio cannot be asymptotically tractable. To attack this difficulty we propose a bias correction to achieve the standard χ2-limit. The bias-corrected empirical likelihood ratio shares some of the desired features of the existing least squares method: the estimation of the parameters is not needed; when estimating nonparametric functions in the model, undersmoothing for ensuring √n-consistency of the estimator of the parameters is avoided; the bias-corrected empirical likelihood is self-scale invariant and no plug-in estimator for the limiting variance is needed. Furthermore, since the index is of norm 1, we use this constraint as information to increase the accuracy of the confidence regions (smaller regions at the same nominal level). As a by-product, our approach of using bias correction may also shed light on nonparametric estimation in model checking for other semiparametric regression models. A simulation study is carried out to assess the performance of the bias-corrected empirical likelihood. An application to a real data set is illustrated.

Original languageEnglish
Pages (from-to)549-570
Number of pages22
JournalJournal of the Royal Statistical Society. Series B: Statistical Methodology
Issue number3
Publication statusPublished - Jun 2006

Scopus Subject Areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

User-Defined Keywords

  • Confidence region
  • Coverage probability
  • Empirical likelihood
  • Partially linear single-index models
  • X-distribution


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