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 language | English (US) |
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Pages (from-to) | 191-207 |
Number of pages | 17 |
Journal | Journal of Statistical Planning and Inference |
Volume | 121 |
Issue number | 2 |
DOIs | |
State | Published - Apr 1 2004 |
Externally published | Yes |
Keywords
- Bayes risk
- Contamination
- Frequentist risk
- Mixture
- Robustness
- t-prior
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty
- Applied Mathematics