Integrated likelihood functions for non-Bayesian inference

Thomas A Severini*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

32 Scopus citations

Abstract

Consider a model with parameter = (, ), where is the parameter of interest, and let L(, ) denote the likelihood function. One approach to likelihood inference for is to use an integrated likelihood function, in which is eliminated from L(, ) by integrating with respect to a density function (|). The goal of this paper is to consider the problem of selecting (|) so that the resulting integrated likelihood function is useful for non-Bayesian likelihood inference. The desirable properties of an integrated likelihood function are analyzed and these suggest that (|) should be chosen by finding a nuisance parameter that is unrelated to and then taking the prior density for to be independent of . Such an unrelated parameter is constructed and the resulting integrated likelihood is shown to be closely related to the modified profile likelihood.

Original languageEnglish (US)
Pages (from-to)524-542
Number of pages19
JournalBiometrika
Volume94
Issue number3
DOIs
StatePublished - Sep 14 2007

Keywords

  • Modified profile likelihood
  • Nuisance parameter
  • Orthogonal parameters
  • Reference prior

ASJC Scopus subject areas

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

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