The Annals of Statistics

Admissible Confidence Interval and Point Estimation for Translation or Scale Parameters

Arthur Cohen and William E. Strawderman

Full-text: Open access

Abstract

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

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

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176342421

Digital Object Identifier
doi:10.1214/aos/1176342421

Mathematical Reviews number (MathSciNet)
MR359111

Zentralblatt MATH identifier
0258.62006

JSTOR
links.jstor.org

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

Keywords
Confidence intervals admissibility minimax translation parameter scale parameter

Citation

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. https://projecteuclid.org/euclid.aos/1176342421


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