The Annals of Statistics

A Necessary Condition for Admissibility

Lawrence D. Brown

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Abstract

The main theorem of this note is required in a paper of Brown. Briefly, the theorem shows that procedures which can be improved on in a neighborhood of infinity are either inadmissible or are generalized Bayes for a (possibly improper) prior whose rate of growth at infinity is of an appropriate order. This theorem is applied here to show that the risk of the usual estimator of a two dimensional normal mean, $\theta$, cannot be improved on near $\infty$ at order $\|\theta\|^{-2}$.

Article information

Source
Ann. Statist., Volume 8, Number 3 (1980), 540-544.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176345007

Digital Object Identifier
doi:10.1214/aos/1176345007

Mathematical Reviews number (MathSciNet)
MR568719

Zentralblatt MATH identifier
0444.62013

JSTOR
links.jstor.org

Subjects
Primary: 62C15: Admissibility
Secondary: 62C07: Complete class results 62C10: Bayesian problems; characterization of Bayes procedures

Keywords
Admissibility generalized Bayes procedures

Citation

Brown, Lawrence D. A Necessary Condition for Admissibility. Ann. Statist. 8 (1980), no. 3, 540--544. doi:10.1214/aos/1176345007. https://projecteuclid.org/euclid.aos/1176345007


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