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Estimated confidence under the validity constraint. (English) Zbl 0755.62007
The decision theoretic estimated confidence approach is examined. Particular attention is paid to results under the frequentist validity constraint $$E\sb \theta I(\theta\in C\sb X) \ge E\sb \theta\gamma(X),$$ where $\gamma(X)$ is a data dependent estimate of the value of the coverage function $I(\theta\in C\sb X)$ and $C\sb X$ is a confidence set for the parameter $\theta$ based on the random variable $X$. The main result shows that the usual constant coverage probability estimator for the usual confidence set of a linear model is admissible under the frequentist validity constraint. The matter of inadmissibility without this constraint is also discussed.
Reviewer: A.Dale (Durban)

MSC:
62A01Foundations and philosophical topics in statistics
62F25Parametric tolerance and confidence regions
62C05General considerations in statistical decision theory
62C15Statistical admissibility
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