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March, 1977 Convex Sets of Finite Population Plans
H. P. Wynn
Ann. Statist. 5(2): 414-418 (March, 1977). DOI: 10.1214/aos/1176343809


Let $P_1$ be a finite population sampling plan and $V$ a collection of subsets of units. The inclusion probabilities for members of $V$ may be calculated. For example, if $V$ comprises all single units and pairs of units we obtain all first and second order inclusion probabilities $\pi_i, \pi_{ij}$. Another plan $P_2$ is called equivalent to $P_1$ with respect to $V$ if the corresponding inclusion probabilities for $P_1$ are equal to those for $P_2$. However, $P_2$ may have fewer samples with positive probability of selection, that is to say smaller "support." An upper bound is put on the minimum support size of all such $P_2$. For $P_1$ simple random sampling, some examples are given for $P_2$ with small support.


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H. P. Wynn. "Convex Sets of Finite Population Plans." Ann. Statist. 5 (2) 414 - 418, March, 1977.


Published: March, 1977
First available in Project Euclid: 12 April 2007

zbMATH: 0365.62012
MathSciNet: MR518633
Digital Object Identifier: 10.1214/aos/1176343809

Primary: 62D05

Rights: Copyright © 1977 Institute of Mathematical Statistics


Vol.5 • No. 2 • March, 1977
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