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September, 1977 A Conditional Confidence Principle
James V. Bondar
Ann. Statist. 5(5): 881-891 (September, 1977). DOI: 10.1214/aos/1176343944

Abstract

A conditional confidence property is examined in the context of invariant statistical models, for set estimators of equivariant functions of the parameter. Set estimators deduced from likelihood considerations are then identical to Bayes credible sets induced from a right invariant prior. It is shown that amenability of the group ensures that these intervals satisfy a betting interpretation of confidence sets due essentially to Buehler and Tukey. As a corollary, a level $\alpha$ Bayes set estimator is of level at-most-$\alpha$ as a Neyman-Pearson confidence interval if the group is amenable.

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James V. Bondar. "A Conditional Confidence Principle." Ann. Statist. 5 (5) 881 - 891, September, 1977. https://doi.org/10.1214/aos/1176343944

Information

Published: September, 1977
First available in Project Euclid: 12 April 2007

zbMATH: 0366.62002
MathSciNet: MR451472
Digital Object Identifier: 10.1214/aos/1176343944

Subjects:
Primary: 62A05
Secondary: 62A15

Keywords: Bayes set estimator , conditional confidence , relevant subset

Rights: Copyright © 1977 Institute of Mathematical Statistics

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Vol.5 • No. 5 • September, 1977
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