The likelihood ratio approximation to the conditional distribution of the maximum likelihood estimator in the discrete case

Thomas A. Severini*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

The likelihood ratio approximation, also called Barndorff-Nielsen's approximation and often denoted by p*, provides a highly accurate approximation to the conditional density of a maximum likelihood estimator θ̂ given an ancillary statistic. In this paper, the properties of p* are considered for the case in which the underlying random variables have a lattice distribution and θ̂ has a discrete, but not necessarily lattice, distribution. If θ̂ has a lattice distribution, then p* provides a valid approximation to the density of θ̂ with respect to counting measure. If the distribution of θ̂ is non-lattice, then p* is still a valid approximation to the conditional density of θ̂; however, the dominating measure is no longer counting measure.

Original languageEnglish (US)
Pages (from-to)939-945
Number of pages7
JournalBiometrika
Volume87
Issue number4
DOIs
StatePublished - Jan 1 2000

Keywords

  • Ancillary statistic
  • Asymptotic theory
  • Lattice distribution
  • Likelihood
  • Maximum likelihood estimator

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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