Likelihood ratio statistics based on an integrated likelihood

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10 Scopus citations

Abstract

An integrated likelihood depends only on the parameter of interest and the data, so it can be used as a standard likelihood function for likelihood-based inference. In this paper, the higher-order asymptotic properties of the signed integrated likelihood ratio statistic for a scalar parameter of interest are considered. These results are used to construct a modified integrated likelihood ratio statistic and to suggest a class of prior densities to use in forming the integrated likelihood. The properties of the integrated likelihood ratio statistic are compared to those of the standard likelihood ratio statistic. Several examples show that the integrated likelihood ratio statistic can be a useful alternative to the standard likelihood ratio statistic.

Original languageEnglish (US)
Pages (from-to)481-496
Number of pages16
JournalBiometrika
Volume97
Issue number2
DOIs
StatePublished - Jun 1 2010

Keywords

  • Confidence interval
  • Higher-order asymptotic theory
  • Hypothesis test
  • Modified signed likelihood ratio statistic
  • Nuisance parameter
  • Power

ASJC Scopus subject areas

  • 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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