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March, 1973 On Some Difficulties in a Frequency Theory of Inference
Donald A. Pierce
Ann. Statist. 1(2): 241-250 (March, 1973). DOI: 10.1214/aos/1176342362


A study of relationships between confidence regions being Bayesian, and the existence of some generalizations of Fisher's notion of relevant subsets. For a betting scheme introduced by Buehler, and for finite parameter space, it is shown that non-Bayesian procedures allow a winning strategy for a statistician's adversary. It is further shown, for finite parameter space, non-Bayesian procedures must admit conditional confidence levels bounded away from the unconditional level, the converse to a theorem of Wallace. For general parameter space these results follow from a procedure not being weak Bayes in a certain sense.


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Donald A. Pierce. "On Some Difficulties in a Frequency Theory of Inference." Ann. Statist. 1 (2) 241 - 250, March, 1973.


Published: March, 1973
First available in Project Euclid: 12 April 2007

zbMATH: 0326.62010
MathSciNet: MR359103
Digital Object Identifier: 10.1214/aos/1176342362

Rights: Copyright © 1973 Institute of Mathematical Statistics


Vol.1 • No. 2 • March, 1973
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