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December, 1991 Estimated Confidence Under the Validity Constraint
Jiunn T. Hwang, Lawrence D. Brown
Ann. Statist. 19(4): 1964-1977 (December, 1991). DOI: 10.1214/aos/1176348381


We examine the decision theoretic estimated confidence approach proposed by Kiefer, Robinson and Berger, and focus on results under the frequentist validity constraint previously described by Brown and by Berger. Our main result is that the usual constant coverage probability estimator for the usual confidence set of a linear model is admissible under the frequentist validity constraint. Note that it is inadmissible without the frequentist validity constraint when the dimension is at least 5. The criterion of admissibility under the frequentist validity constraint is shown to be quite a reasonable one. Therefore the constant coverage probability estimator which has been widely used is justifiable from the post-data point of view.


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Jiunn T. Hwang. Lawrence D. Brown. "Estimated Confidence Under the Validity Constraint." Ann. Statist. 19 (4) 1964 - 1977, December, 1991.


Published: December, 1991
First available in Project Euclid: 12 April 2007

zbMATH: 0755.62007
MathSciNet: MR1135159
Digital Object Identifier: 10.1214/aos/1176348381

Primary: 62A20
Secondary: 62C05 , 62C15 , 62F25

Keywords: coverage probability , decision theory , relevant subsets , usual confidence set , validity admissibility

Rights: Copyright © 1991 Institute of Mathematical Statistics

Vol.19 • No. 4 • December, 1991
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