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December, 1987 Conditionally Acceptable Recentered Set Estimators
George Casella
Ann. Statist. 15(4): 1363-1371 (December, 1987). DOI: 10.1214/aos/1176350598

Abstract

The usual confidence sphere for a multivariate normal mean can be uniformly improved upon, in terms of coverage probability, by recentering it at a Stein-type estimator. However, these improved sets can have poor conditional performance. Using the theory of relevant betting procedures, which provides an objective means for assessing the conditional performance of a statistical procedure, a criterion for conditional acceptability can be established. A method of constructing such sets is outlined and applied to some recentered confidence sets. In particular, recentering at the positive-part James-Stein estimator yields a conditionally acceptable confidence set.

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George Casella. "Conditionally Acceptable Recentered Set Estimators." Ann. Statist. 15 (4) 1363 - 1371, December, 1987. https://doi.org/10.1214/aos/1176350598

Information

Published: December, 1987
First available in Project Euclid: 12 April 2007

zbMATH: 0629.62013
MathSciNet: MR913562
Digital Object Identifier: 10.1214/aos/1176350598

Subjects:
Primary: 62C99
Secondary: 62F10

Rights: Copyright © 1987 Institute of Mathematical Statistics

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Vol.15 • No. 4 • December, 1987
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