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Fast integer-valued algorithms for optimal allocations under constraints in stratified sampling

Author

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  • Friedrich, Ulf
  • Münnich, Ralf
  • de Vries, Sven
  • Wagner, Matthias

Abstract

In stratified random sampling, minimizing the variance of a total estimate leads to the optimal allocation. However, in practice, this original method is scarcely appropriate since in many applications additional constraints have to be considered. Three optimization algorithms are presented that solve the integral allocation problem with upper and lower bounds. All three algorithms exploit the fact that the feasible region is a polymatroid and share the important feature of computing the globally optimal integral solution, which generally differs from a solution obtained by rounding. This is in contrast to recent references which, in general, treat the continuous relaxation of the optimization problem. Two algorithms are of polynomial complexity and all of them are fast enough to be applied to complex problems such as the German Census 2011 allocation problem with almost 20,000 strata.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:csdana:v:92:y:2015:i:c:p:1-12
    DOI: 10.1016/j.csda.2015.06.003
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    References listed on IDEAS

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    Cited by:

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    2. Jan Pablo Burgard & Ralf Münnich & Martin Rupp, 2020. "Qualitätszielfunktionen für stark variierende Gemeindegrößen im Zensus 2021 [Quality measures respecting highly varying community sizes within the 2021 German Census]," AStA Wirtschafts- und Sozialstatistisches Archiv, Springer;Deutsche Statistische Gesellschaft - German Statistical Society, vol. 14(1), pages 5-65, March.
    3. Martijn H. H. Schoot Uiterkamp & Marco E. T. Gerards & Johann L. Hurink, 2022. "On a Reduction for a Class of Resource Allocation Problems," INFORMS Journal on Computing, INFORMS, vol. 34(3), pages 1387-1402, May.
    4. Ralf Münnich & Jan Pablo Burgard & Siegfried Gabler & Matthias Ganninger & Jan-Philipp Kolb, 2016. "Small Area Estimation In The German Census 2011," Statistics in Transition New Series, Polish Statistical Association, vol. 17(1), pages 25-40, March.
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    6. Wesołowski Jacek, 2019. "Multi-Domain Neyman-Tchuprov Optimal Allocation," Statistics in Transition New Series, Statistics Poland, vol. 20(4), pages 1-12, December.
    7. Münnich Ralf & Burgard Jan Pablo & Gabler Siegfried & Ganninger Matthias & Kolb Jan-Philipp, 2016. "Small Area Estimation in the German Census 2011," Statistics in Transition New Series, Statistics Poland, vol. 17(1), pages 25-40, March.
    8. Jacek Wesołowski, 2019. "Multi-Domain Neyman-Tchuprov Optimal Allocation," Statistics in Transition New Series, Polish Statistical Association, vol. 20(4), pages 1-12, December.
    9. Ralf Münnich & Siegfried Gabler & Christian Bruch & Jan Pablo Burgard & Tobias Enderle & Jan-Philipp Kolb & Thomas Zimmermann, 2015. "Tabellenauswertungen im Zensus unter Berücksichtigung fehlender Werte," AStA Wirtschafts- und Sozialstatistisches Archiv, Springer;Deutsche Statistische Gesellschaft - German Statistical Society, vol. 9(3), pages 269-304, December.
    10. Ravichandran Arun & Pashley Nicole E. & Libgober Brian & Dasgupta Tirthankar, 2024. "Optimal allocation of sample size for randomization-based inference from 2K factorial designs," Journal of Causal Inference, De Gruyter, vol. 12(1), pages 1-18, January.

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