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September, 1984 Optimal Fixed Size Confidence Procedures for a Restricted Parameter Space
Mehmet Zeytinoglu, Max Mintz
Ann. Statist. 12(3): 945-957 (September, 1984). DOI: 10.1214/aos/1176346713


Optimal fixed size confidence procedures are derived for the mean of a normal random variable with known variance, when the mean is restricted to a compact interval. These confidence procedures are, in turn, based on the solution of a related minimax decision problem which is characterized by a zero-one loss function and a compact interval parameter space. The minimax rules obtained are nonrandomized, admissible, Bayes procedures. The decision-theoretic results are extended in two ways: (i) structurally similar (admissible) Bayes minimax rules are also obtained when the sampling distribution has a density function which is unimodal, symmetric about the location parameter and possesses a (strictly) monotone likelihood ratio; (ii) structurally similar minimax rules (minimax within the class of nonrandomized, odd, monotone procedures) are again obtained when the assumption of a monotone likelihood ratio is relaxed.


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Mehmet Zeytinoglu. Max Mintz. "Optimal Fixed Size Confidence Procedures for a Restricted Parameter Space." Ann. Statist. 12 (3) 945 - 957, September, 1984.


Published: September, 1984
First available in Project Euclid: 12 April 2007

zbMATH: 0562.62032
MathSciNet: MR751284
Digital Object Identifier: 10.1214/aos/1176346713

Primary: 62F25
Secondary: 62C20

Rights: Copyright © 1984 Institute of Mathematical Statistics


Vol.12 • No. 3 • September, 1984
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