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September, 1983 Improving on Inadmissible Estimators in the Control Problem
L. Mark Berliner
Ann. Statist. 11(3): 814-826 (September, 1983). DOI: 10.1214/aos/1176346248

Abstract

Let $X$ have a $p$-variate normal distribution with unknown mean $\theta$ and identity covariance matrix. The following transformed version of a control problem (Zaman, 1981) is considered: estimate $\theta$ by $d$ subject to incurring a loss $L(d, \theta) = (\theta^t d - 1)^2$. The comparison of decision rules in terms of expected loss is reduced to the study of differential inequalities. Results establishing the minimaxity of a large class of estimators are obtained. Special attention is given to the proposition of admissible, generalized Bayes rules which dominate the uniform prior, generalized Bayes controller when $p \geq 5$.

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L. Mark Berliner. "Improving on Inadmissible Estimators in the Control Problem." Ann. Statist. 11 (3) 814 - 826, September, 1983. https://doi.org/10.1214/aos/1176346248

Information

Published: September, 1983
First available in Project Euclid: 12 April 2007

zbMATH: 0525.62009
MathSciNet: MR707932
Digital Object Identifier: 10.1214/aos/1176346248

Subjects:
Primary: 62F10
Secondary: 62C15, 62H99

Rights: Copyright © 1983 Institute of Mathematical Statistics

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Vol.11 • No. 3 • September, 1983
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