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May, 1976 A Special Property of Linear Estimates of the Normal Mean
Glen Meeden
Ann. Statist. 4(3): 649-650 (May, 1976). DOI: 10.1214/aos/1176343473


Let $X$ be a normal random variable with mean $\theta$ and variance 1 and consider the problem of estimating $\theta$ with squared error loss. If $\delta(x) = ax + b$ is a linear estimate with $0 \leqq a \leqq 1$ then it is well known that $\lambda\delta$ is an admissible proper Bayes estimate for $\lambda \in (0, 1)$. That is, all contractions of $\delta$ are proper Bayes estimates. In this note we show that no other estimates have this property.


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Glen Meeden. "A Special Property of Linear Estimates of the Normal Mean." Ann. Statist. 4 (3) 649 - 650, May, 1976.


Published: May, 1976
First available in Project Euclid: 12 April 2007

zbMATH: 0336.62022
MathSciNet: MR403000
Digital Object Identifier: 10.1214/aos/1176343473

Primary: 62F10
Secondary: 62C10

Keywords: Bayes estimation , linear estimates , normal distribution , quadratic loss

Rights: Copyright © 1976 Institute of Mathematical Statistics

Vol.4 • No. 3 • May, 1976
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