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July, 1981 A Complete Class Theorem for the Control Problem and Further Results on Admissibility and Inadmissibility
Asad Zaman
Ann. Statist. 9(4): 812-821 (July, 1981). DOI: 10.1214/aos/1176345521

Abstract

The following decision problem is studied. The statistician observes a random $n$-vector $y$ normally distributed with mean $\beta$ and identity covariance matrix. He takes action $\delta\in\mathbb{R}^n$ and suffers the loss $L(\beta, \delta) = (\beta'\delta - 1)^2.$ It is shown that this is equivalent to the linear control problem and closely related to the calibration problem. Among the invariant estimators, it is shown that the formal Bayes rules together with some of their limits include all admissible invariant rules. Other results on admissibility and inadmissibility of some commonly used estimators for the problem are obtained.

Citation

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Asad Zaman. "A Complete Class Theorem for the Control Problem and Further Results on Admissibility and Inadmissibility." Ann. Statist. 9 (4) 812 - 821, July, 1981. https://doi.org/10.1214/aos/1176345521

Information

Published: July, 1981
First available in Project Euclid: 12 April 2007

zbMATH: 0504.62008
MathSciNet: MR619284
Digital Object Identifier: 10.1214/aos/1176345521

Subjects:
Primary: 62C07
Secondary: 62C10 , 62C15

Keywords: Admissibility , complete class , control problem , formal Bayes , Invariance

Rights: Copyright © 1981 Institute of Mathematical Statistics

Vol.9 • No. 4 • July, 1981
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