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January, 1978 A Contribution to Kiefer's Theory of Conditional Confidence Procedures
Lawrence D. Brown
Ann. Statist. 6(1): 59-71 (January, 1978). DOI: 10.1214/aos/1176344065


The "procedures" discussed in this paper are of the following type: The statistician makes a conventional decision (in a multiple decision problem). He also provides a statement of the guaranteed conditional probability that his decision will be correct, given the observed value of some conditioning random variable. Various admissibility criteria to relate such procedures are proposed. For example, we say that one procedure is better (first sense) than a second if the guaranteed conditional confidence statement using the first is stochastically larger than that using the second, for all possible states of nature. Some ramifications of these admissibility criteria are discussed, and some specific admissible procedures are described for problems with two possible states of nature. In particular, the procedure having the finest possible monotone conditioning and having equal conditional confidence under both states of nature is shown to have many desirable admissibility properties.


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Lawrence D. Brown. "A Contribution to Kiefer's Theory of Conditional Confidence Procedures." Ann. Statist. 6 (1) 59 - 71, January, 1978.


Published: January, 1978
First available in Project Euclid: 12 April 2007

zbMATH: 0383.62008
MathSciNet: MR471160
Digital Object Identifier: 10.1214/aos/1176344065

Keywords: A99 , C05 , C99 , Conditional confidence procedures , F07 , guaranteed conditional confidence

Rights: Copyright © 1978 Institute of Mathematical Statistics


Vol.6 • No. 1 • January, 1978
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