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June, 1951 Conditional Expectation and the Efficiency of Estimates
Paul G. Hoel
Ann. Math. Statist. 22(2): 299-301 (June, 1951). DOI: 10.1214/aoms/1177729651


A probability density function, $f(x; \theta)$, is considered for which there exists a sufficient statistic. It is shown, under certain regularity conditions on the family of distributions and on the class of estimates, that if there exists an unbiased sufficient estimate of $\theta$, it will be unique. This result is used to show that when the regularity conditions are satisfied, the method of Blackwell for improving an unbiased estimate of $\theta$ merely yields a natural estimate.


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Paul G. Hoel. "Conditional Expectation and the Efficiency of Estimates." Ann. Math. Statist. 22 (2) 299 - 301, June, 1951.


Published: June, 1951
First available in Project Euclid: 28 April 2007

zbMATH: 0054.06202
MathSciNet: MR42648
Digital Object Identifier: 10.1214/aoms/1177729651

Rights: Copyright © 1951 Institute of Mathematical Statistics

Vol.22 • No. 2 • June, 1951
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