Open Access
June, 1960 Estimating the Mean of a Finite Population
J. Roy, I. M. Chakravarti
Ann. Math. Statist. 31(2): 392-398 (June, 1960). DOI: 10.1214/aoms/1177705901


In sampling from a finite population, the nonexistence of a uniformly minimum variance unbiased estimator for the mean $\mu$ has been demonstrated by Godambe [3], and the inadmissibility of the sample mean as an estimator for $\mu$, when sampling is with replacement and equal probabilities, has been proved by Des Raj and Khamis [2] and by Basu [1]. In this paper, the problem of unbiased linear estimation of $\mu$ with minimum variance is considered for a very general scheme of sampling. An admissible estimator is obtained, together with a complete class of estimators. It is shown further that, for a somewhat restricted sampling scheme, amongst estimators with variance proportional to $\sigma^2$, there does exist a best estimator which, in the case of sampling with replacement and equal probabilities, is the same as that considered in [1] and [2].


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J. Roy. I. M. Chakravarti. "Estimating the Mean of a Finite Population." Ann. Math. Statist. 31 (2) 392 - 398, June, 1960.


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

zbMATH: 0093.15801
MathSciNet: MR116409
Digital Object Identifier: 10.1214/aoms/1177705901

Rights: Copyright © 1960 Institute of Mathematical Statistics

Vol.31 • No. 2 • June, 1960
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