The asymptotic efficiency of conditional likelihood methods

Kung Yee Liang

Research output: Contribution to journalArticlepeer-review


This paper concerns the efficiency of the conditional likelihood method for inference in models which include nuisance parameters. A new concept of ancillarity, asymptotic weak ancillarity, is introduced. It is shown that the conditional maximum likelihood estimator and the conditional score test of θ, the parameter of interest, are asymptotically equivalent to their unconditional counterparts, and hence are asymptotically efficient, provided that the conditioning statistic is asymptotically weakly ancillary. The key assumption that the conditioning statistic is asymptotically weakly ancillary is verified when the underlying distribution is from exponential families. Some illustrative examples are given.

Original languageEnglish (US)
Pages (from-to)305-313
Number of pages9
Issue number2
StatePublished - Aug 1 1984


  • Asymptotic efficiency
  • Asymptotic weak ancillarity
  • Conditional likelihood
  • Exponential family
  • Fisher information
  • Nuisance parameter

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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