Local ancillarity in the presence of a nuisance parameter

Thomas A Severini*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

SUMMARY: Approximate ancillarity in the presence of a nuisance parameter is considered. A theory of approximate S-ancillarity, based on the concept of local ancillarity introduced by Cox (1980), is developed. First- and second-order local S-ancillarity are considered in detail and these results are applied to several examples. These examples indicate that, although first-order local S-ancillarity is a weak condition, second-order local S-ancillarity is too strong a requirement for general use. Hence, a second aspect of the paper is a study of the properties of an approximately ancillary statistic that are desirable for inference in the presence of a nuisance parameter; this leads to a weaker definition of local ancillarity in the presence of a nuisance parameter that is satisfied in many cases.

Original languageEnglish (US)
Pages (from-to)305-320
Number of pages16
JournalBiometrika
Volume80
Issue number2
DOIs
StatePublished - Jun 1 1993

Keywords

  • Asymptotic theory
  • Conditional inference
  • Information
  • Likelihood inference
  • Local 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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