Bayes/frequentist compromise decision rules for Gaussian sampling

Lynn E Eberly, Thomas A. Louis

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

Bayesian methods have the potential to confer substantial advantages over frequentist when the assumed prior is approximately correct, but otherwise can perform poorly. Therefore, estimators and other inferences that strike a compromise between Bayes and frequentist optimality are attractive. To evaluate potential trade-offs, we study Bayes vs. frequentist risk under Gaussian sampling for families of point estimators and interval estimators. Bayes/frequentist compromises for interval estimation are more challenging than for point estimation, since performance involves an interplay between coverage and length. Each family allows 'purchasing' improved frequentist performance by allowing a small increase in Bayes risk over the Bayes rule. Any degree of increase can be specified, thus enabling greater or lesser trade-offs between Bayes and frequentist risk.

Original languageEnglish (US)
Pages (from-to)191-207
Number of pages17
JournalJournal of Statistical Planning and Inference
Volume121
Issue number2
DOIs
StatePublished - Apr 1 2004

Keywords

  • Bayes risk
  • Contamination
  • Frequentist risk
  • Mixture
  • Robustness
  • t-prior

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