Estimated Confidence Under the Validity Constraint
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...
| Veröffentlicht in: | The Annals of Statistics. - Institute of Mathematical Statistics. - 19(1991), 4, Seite 1964-1977 |
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| Format: | Online-Aufsatz |
| Sprache: | English |
| Veröffentlicht: |
1991
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| Zugriff auf das übergeordnete Werk: | The Annals of Statistics |
| Schlagworte: | Coverage probability usual confidence set decision theory relevant subsets validity admissibility Mathematics Behavioral sciences Information science Applied sciences |
| Zusammenfassung: | 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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| ISSN: | 00905364 |