The Annals of Statistics

Estimated Confidence Under the Validity Constraint

Jiunn T. Hwang and Lawrence D. Brown

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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.

Article information

Ann. Statist., Volume 19, Number 4 (1991), 1964-1977.

First available in Project Euclid: 12 April 2007

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


Primary: 62A20
Secondary: 62F25: Tolerance and confidence regions 62C05: General considerations 62C15: Admissibility

Coverage probability usual confidence set decision theory relevant subsets validity admissibility


Hwang, Jiunn T.; Brown, Lawrence D. Estimated Confidence Under the Validity Constraint. Ann. Statist. 19 (1991), no. 4, 1964--1977. doi:10.1214/aos/1176348381.

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