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

Liugen Xue*, Lixing ZHU

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

19 Citations (Scopus)

Abstract

In this paper, a partially linear single-index model is investigated, and three empirical log-likelihood ratio statistics for the unknown parameters in the model are suggested. It is proved that the proposed statistics are asymptotically standard chi-square under some suitable conditions, and hence can be used to construct the confidence regions of the parameters. Our methods can also deal with the confidence region construction for the index in the pure single-index model. A simulation study indicates that, in terms of coverage probabilities and average areas of the confidence regions, the proposed methods perform better than the least-squares method.

Original languageEnglish
Pages (from-to)1333-1348
Number of pages16
JournalScience in China, Series A: Mathematics, Physics, Astronomy
Volume48
Issue number10
DOIs
Publication statusPublished - Oct 2005

Scopus Subject Areas

  • Mathematics(all)

User-Defined Keywords

  • Chi-square distribution
  • Confidence region
  • Coverage probability
  • Empirical likelihood
  • Partially linear single-index model

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