Empirical Bayes and conditional inference with many nuisance parameters

Kung Yee Liang, Daniel Tsou

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SUMMARY: This paper concerns the use of empirical Bayes methods to improve the efficiency of a parameter of interest, θ, in the presence of many nuisance parameters, {øi}, one from each data stratum. A class of distributions is introduced such that for fixed θ, the minimal sufficient statistic ti(θ) for øi is from an exponential family and hence complete. By imposing the assumption that the øi's are generated from an unspecified distribution function Q, we show that for this class of distributions the conditional score function for θ (Lindsay, 1982) with oslhasi estimated by EQ{oslhasi /ti(θ)} is optimal in a sense similar to that of Cox & Reid (1987) and Liang (1987). Two empirical Bayes estimates of ø, along with the maximum likelihood estimate of øi are compared through simulations in terms of θ estimation.

Original languageEnglish (US)
Pages (from-to)261-270
Number of pages10
Issue number2
Publication statusPublished - Jun 1992



  • Conditional score function
  • Conjugate prior
  • Empirical Bayes
  • Linear Bayes
  • Maximum likelihood estimate
  • Nuisance parameters

ASJC Scopus subject areas

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

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