The Annals of Statistics

Admissible Confidence Interval and Point Estimation for Translation or Scale Parameters

Arthur Cohen and William E. Strawderman

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Sufficient conditions for admissibility of the best invariant confidence interval for a translation or scale parameter are given, for a very wide class of loss functions. These conditions result by adapting a theorem of L. D. Brown [2]. Simpler sufficient conditions are found for a subclass of loss functions of special interest. The subclass of losses involves three components. One concerned with coverage of the true value, another concerned with the distance from the interval end points to the true parameter, and a third concerned with length of the interval. Such a loss function unifies confidence interval and point estimation in the sense that if an optimality property holds for all loss functions in the subclass, then the optimality property holds for typical confidence interval problems and typical point estimation problems.

Article information

Ann. Statist., Volume 1, Number 3 (1973), 545-550.

First available in Project Euclid: 12 April 2007

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


Primary: 62C15: Admissibility
Secondary: 62F10: Point estimation 62G05: Estimation

Confidence intervals admissibility minimax translation parameter scale parameter


Cohen, Arthur; Strawderman, William E. Admissible Confidence Interval and Point Estimation for Translation or Scale Parameters. Ann. Statist. 1 (1973), no. 3, 545--550. doi:10.1214/aos/1176342421.

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