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Combining random sampling and census strategies - Justification of inclusion probabilities equal to 1

Author

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  • Horst Stenger
  • Siegfried Gabler

Abstract

Very often values of a size variable are known for the elements of a population we want to sample. For example, the elements may be clusters, the size variable denoting the number of units in a cluster. Then, it is quite usual to base the selection of elements on inclusion probabilities which are proportionate to the size values. To estimate the total of all values of an unknown variable for the units in the population of interest (i.e. for the units contained in the clusters) we may use weights, e.g. inverse inclusion probabilities. We want to clarify these ideas by the minimax principle. Especially, we will show that the use of inclusion probabilities equal to 1 is recommendable for units with high values of the size measure. Copyright Springer-Verlag 2005

Suggested Citation

  • Horst Stenger & Siegfried Gabler, 2005. "Combining random sampling and census strategies - Justification of inclusion probabilities equal to 1," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 61(2), pages 137-156, April.
    • Handle: RePEc:spr:metrik:v:61:y:2005:i:2:p:137-156
    DOI: 10.1007/s001840400328
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    Citations

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    Cited by:

    1. Friedrich, Ulf & Münnich, Ralf & de Vries, Sven & Wagner, Matthias, 2015. "Fast integer-valued algorithms for optimal allocations under constraints in stratified sampling," Computational Statistics & Data Analysis, Elsevier, vol. 92(C), pages 1-12.
    2. Ralf Münnich & Ekkehard Sachs & Matthias Wagner, 2012. "Numerical solution of optimal allocation problems in stratified sampling under box constraints," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 96(3), pages 435-450, July.
    3. M. G. M. Khan & Jacek Wesołowski, 2019. "Neyman-type sample allocation for domains-efficient estimation in multistage sampling," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 103(4), pages 563-592, December.
    4. Siegfried Gabler & Matthias Ganninger & Ralf Münnich, 2012. "Optimal allocation of the sample size to strata under box constraints," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 75(2), pages 151-161, February.

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