On the approximate elimination of nuisance parameters by conditioning

Thomas A Severini*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

SUMMARY: The general problem of inference about a scalar parameter of interest θ in the presence of a nuisance parameter λ using conditional inference is considered.xml. A condition is given under which inference based on the conditional distribution of θ, the maximum likelihood estimate of θ, given λo, the maximum likelihood estimate of λ for fixed θ = θ0, is optimal, in a certain sense. When this condition is not satisfied, it is shown that inference should be based on the conditional distribution of θ given λo, jo where jo denotes the observed information for λ for fixed θ =θθo, although this will involve some loss of information about θ. This information loss is shown to be related to the statistical curvature of the model.

Original languageEnglish (US)
Pages (from-to)649-661
Number of pages13
JournalBiometrika
Volume81
Issue number4
DOIs
StatePublished - Dec 1 1994

Keywords

  • Asymptotic theory
  • Conditional inference
  • Information
  • Likelihood inference
  • Local inference
  • Observed information
  • Statistical curvature

ASJC Scopus subject areas

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

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