The Annals of Mathematical Statistics
- Ann. Math. Statist.
- Volume 20, Number 3 (1949), 426-432.
On the Determination of Optimum Probabilities in Sampling
In a previous paper  it was shown that it is sometimes profitable to select sampling units with probability proportionate to size of the unit. This note indicates a method of determining the probabilities of selection which minimize the variance of the sample estimate at a fixed cost. Some approximations that have practical applications are given.
Ann. Math. Statist., Volume 20, Number 3 (1949), 426-432.
First available in Project Euclid: 28 April 2007
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Hansen, Morris H.; Hurwitz, William N. On the Determination of Optimum Probabilities in Sampling. Ann. Math. Statist. 20 (1949), no. 3, 426--432. doi:10.1214/aoms/1177729994. https://projecteuclid.org/euclid.aoms/1177729994