The Annals of Statistics

Conditionally Acceptable Recentered Set Estimators

George Casella

Full-text: Open access

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.

Article information

Source
Ann. Statist., Volume 15, Number 4 (1987), 1363-1371.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176350598

Digital Object Identifier
doi:10.1214/aos/1176350598

Mathematical Reviews number (MathSciNet)
MR913562

Zentralblatt MATH identifier
0629.62013

JSTOR
links.jstor.org

Subjects
Primary: 62C99: None of the above, but in this section
Secondary: 62F10: Point estimation

Keywords
Betting procedures confidence sets multivariate normal

Citation

Casella, George. Conditionally Acceptable Recentered Set Estimators. Ann. Statist. 15 (1987), no. 4, 1363--1371. doi:10.1214/aos/1176350598. https://projecteuclid.org/euclid.aos/1176350598


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