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September, 1982 Towards a Calculus for Admissibility
Andrzej Kozek
Ann. Statist. 10(3): 825-837 (September, 1982). DOI: 10.1214/aos/1176345874


It is shown how the calculus can be used to characterize admissible decision rules (Pareto optimal points, efficient points). Necessary and sufficient conditions for admissibility are derived in terms of the first and the second directional derivatives of convex risk functions. In particular, the results obtained imply that if $p$ is to be estimated in the binomial distribution $B(n, p)$, then an estimator is admissible for the quadratic loss function if and only if it fulfills some analytic conditions.


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Andrzej Kozek. "Towards a Calculus for Admissibility." Ann. Statist. 10 (3) 825 - 837, September, 1982.


Published: September, 1982
First available in Project Euclid: 12 April 2007

zbMATH: 0498.62010
MathSciNet: MR663435
Digital Object Identifier: 10.1214/aos/1176345874

Primary: 62C15
Secondary: 49B99 , 90A05

Keywords: Admissibility , Binomial distribution , convex transformation , efficiency , Pareto optimality

Rights: Copyright © 1982 Institute of Mathematical Statistics

Vol.10 • No. 3 • September, 1982
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