An empirical adjustment to the likelihood ratio statistic

Thomas A. Severini*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

36 Scopus citations


Consider a model parameterised by a scalar parameter of interest ψ and a nuisance parameter λ Inference about ψ may be based on the signed square root of the likelihood ratio statistic, R. The statistic R is asymptotically distributed according to a standard normal distribution, with error O(n-1/2). To reduce the error of this normal approximation, several modifications to R have been proposed such as Barndorff-Nielsen's modified directed likelihood statistic, R*. In this paper, an approximation to R* is proposed that can be calculated numerically for a wide range of models. This approximation is shown to agree with R* with error of order Op(n-1). The results are illustrated on several examples.

Original languageEnglish (US)
Pages (from-to)235-247
Number of pages13
Issue number2
StatePublished - 1999


  • ABC interval
  • Conditional inference
  • Confidence limits
  • Directed likelihood-ratio

ASJC Scopus subject areas

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


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