Date of this Version
The Annals of Statistics
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.
coverage probability, usual confidence set, decision theory, relevant subsets, validity admissibility
Hwang, J. T., & Brown, L. D. (1991). Estimated Confidence Under the Validity Constraint. The Annals of Statistics, 19 (4), 1964-1977. http://dx.doi.org/10.1214/aos/1176348381
Date Posted: 27 November 2017
This document has been peer reviewed.