Empirical likelihood in the presence of nuisance parameters

Nicole A. Lazar, Per Aslak Mykland

Research output: Contribution to journalArticlepeer-review

20 Scopus citations

Abstract

Empirical likelihood was introduced as a nonparametric analogue of ordinary parametric likelihood. It is well known that the empirical likelihood ratio statistic inherits a number of properties of the parametric likelihood ratio statistic, such as the asymptotic chi-squared distribution and Bartlett correctability. This raises the question of whether or not the same is true in the presence of nuisance parameters. Recent work by Qin & Lawless (1994) indicates that the chi-squared distribution is still valid to first order. We show that, when nuisance parameters are present, as introduced via a system of estimating equations, the asymptotic expansion for the signed square root of the empirical likelihood ratio statistic has a nonstandard form. This implies that the empirical likelihood ratio statistic itself does not permit a Bartlett correction.

Original languageEnglish (US)
Pages (from-to)203-211
Number of pages9
JournalBiometrika
Volume86
Issue number1
DOIs
StatePublished - 1999

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Mathematics(all)
  • Agricultural and Biological Sciences (miscellaneous)
  • Agricultural and Biological Sciences(all)
  • Statistics, Probability and Uncertainty
  • Applied Mathematics

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