The Annals of Statistics

Optimal Fixed Size Confidence Procedures for a Restricted Parameter Space

Mehmet Zeytinoglu and Max Mintz

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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.

Article information

Ann. Statist., Volume 12, Number 3 (1984), 945-957.

First available in Project Euclid: 12 April 2007

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


Primary: 62F25: Tolerance and confidence regions
Secondary: 62C20: Minimax procedures

Confidence procedures minimax procedures zero-one loss restricted parameter space


Zeytinoglu, Mehmet; Mintz, Max. Optimal Fixed Size Confidence Procedures for a Restricted Parameter Space. Ann. Statist. 12 (1984), no. 3, 945--957. doi:10.1214/aos/1176346713.

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