A simple general formula for tail probabilities for frequentist and Bayesian inference

D. A.S. Fraser, N. Reid, J. Wu

Research output: Contribution to journalArticlepeer-review

94 Scopus citations

Abstract

We describe a simple general formula for approximating the p-value for testing a scalar parameter in the presence of nuisance parameters. The formula covers both frequentist and Bayesian contexts and does not require explicit nuisance parameterisation. Implementation is discussed in terms of computer algebra packages. Examples are given and the relationship to Barndorff-Nielsen's approximation is discussed.

Original languageEnglish
Pages (from-to)249-264
Number of pages16
JournalBiometrika
Volume86
Issue number2
DOIs
StatePublished - 1999

Keywords

  • Asymptotic theory
  • Likelihood method
  • Pivotal quantity
  • Tail probability
  • Third-order inference

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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