Note on a fundamental relationship between admissible and Bayesian decision rules

M. Asgharian, S. Noorbaloochi

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

Using the basic separation theorem and the Riesz representation theorem we give a simple proof that any admissible rule for compact and certain non-compact parameter spaces is a Bayes rule. The result is employed to show that under suitable conditions any admissible rule δ = ⊗i=1n δi is a Bayes rule against some proper prior π = ⊗i=1n πi where πi are proper priors of δi. We will also apply these theorems in both the parametric and non-parametric settings.

Original languageEnglish (US)
Pages (from-to)21-34
Number of pages14
JournalStatistics
Volume31
Issue number1
DOIs
StatePublished - 1998

Keywords

  • Admissibility
  • Bayes rules
  • Fundamental theorem of decision theory

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