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September, 1976 On Uniformly Minimum Variance Estimation in Finite Populations
Carl Erik Sarndal
Ann. Statist. 4(5): 993-997 (September, 1976). DOI: 10.1214/aos/1176343598


In the literature one finds (at least) two approaches towards proving that the sample mean is uniformly minimum variance (UMV), among unbiased estimates that "ignore the labels," for the finite population mean: The "traditional approach" and the "scale-load approach." The identity of results under the two approaches extends to a more general setting, as shown in this paper: The Horvitz-Thompson estimate is UMV unbiased for any given fixed effective size design.


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Carl Erik Sarndal. "On Uniformly Minimum Variance Estimation in Finite Populations." Ann. Statist. 4 (5) 993 - 997, September, 1976.


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

zbMATH: 0363.62026
MathSciNet: MR413318
Digital Object Identifier: 10.1214/aos/1176343598

Primary: 62005
Secondary: 62F10

Keywords: completeness , estimation , Horvitz-Thompson estimator , labels , scale-loads , sufficiency , uniformly minimum variance

Rights: Copyright © 1976 Institute of Mathematical Statistics

Vol.4 • No. 5 • September, 1976
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