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https://hdl.handle.net/2142/21448
Description
Title
Admissibility ofp-value rules
Author(s)
Thompson, Peter Michael
Issue Date
1989
Doctoral Committee Chair(s)
Marden, John I.
Department of Study
Statistics
Discipline
Statistics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Statistics
Language
eng
Abstract
This work deals with a decision-theoretic evaluation of p-value rules. A test statistic is judged on the behavior of its p-value with the loss function being an increasing function G of the p-value.
Examples are presented in which every fixed-level test based on a statistic is admissible, but the corresponding p-value is inadmissible. It is also shown that if a statistic has an admissible p-value, all of its corresponding fixed-level tests are admissible.
In addition, Bayes p-values are investigated. It is shown that Bayes p-values and their weak limits form an essentially complete class. Also, the set of p-values which are Bayes typically does not depend on the particular loss function G being used.
Finally, the case where the parameter space is compact is looked into. A characterization is given of an essentially complete class of p-values.
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