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September, 1960 Estimates with Prescribed Variance Based on Two-Stage Sampling
Allan Birnbaum, William C. Healy Jr.
Ann. Math. Statist. 31(3): 662-676 (September, 1960). DOI: 10.1214/aoms/1177705793


A method is given which provides, under conditions satisfied by many common distributions, rules for sampling in two stages so as to obtain an unbiased estimator of a given parameter, having variance equal to, or not exceeding, a prescribed bound. The method is applied to estimation of the means of binomial, Poisson, and hypergeometric distributions; scale-parameters in general and of the Gamma distribution in particular; the variance of a normal distribution; and a component of variance. The use of such estimators to achieve homoscedasticity is discussed. Optimum sampling rules are discussed for some of these estimators, and some tables are given to facilitate their use. The efficiency of the method is shown to be high in many cases.


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Allan Birnbaum. William C. Healy Jr.. "Estimates with Prescribed Variance Based on Two-Stage Sampling." Ann. Math. Statist. 31 (3) 662 - 676, September, 1960.


Published: September, 1960
First available in Project Euclid: 27 April 2007

zbMATH: 0094.14301
MathSciNet: MR117818
Digital Object Identifier: 10.1214/aoms/1177705793

Rights: Copyright © 1960 Institute of Mathematical Statistics

Vol.31 • No. 3 • September, 1960
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