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Numerical solution of optimal allocation problems in stratified sampling under box constraints

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  • Ralf Münnich
  • Ekkehard Sachs
  • Matthias Wagner

Abstract

Modern sampling designs in survey statistics, in general, are constructed in order to optimize the accuracy of estimators such as totals, means and proportions. In stratified random sampling a variance minimal solution was introduced by Neyman and Tschuprov. However, practical constraints may lead to limitations of the domain of sampling fractions which have to be considered within the optimization process. Special attention on the complexity of numerical solutions has to be paid in cases with many strata or when the optimal allocation has to be applied repeatedly, such as in iterative solutions of stratification problems. The present article gives an overview of recent numerical algorithms which allow adequate inclusion of box constraints in the numerical optimization process. These box constraints may play an important role in statistical modeling. Furthermore, a new approach through a fixed point iteration with a finite termination property is presented. Copyright Springer-Verlag 2012

Suggested Citation

  • 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.
    • Handle: RePEc:spr:alstar:v:96:y:2012:i:3:p:435-450
    DOI: 10.1007/s10182-011-0176-z
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    References listed on IDEAS

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    1. 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.
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    Cited by:

    1. Jan Pablo Burgard & Ralf Münnich & Martin Rupp, 2019. "A Generalized Calibration Approach Ensuring Coherent Estimates with Small Area Constraints," Research Papers in Economics 2019-10, University of Trier, Department of Economics.
    2. 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.
    3. repec:csb:stintr:v:17:y:2016:i:1:p:25-40 is not listed on IDEAS
    4. 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.
    5. 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.
    6. Allafi, Sabine & Lohn, Alexandra & Nölting, Christopher & Maier, Alexander, 2022. "Die neue Strukturstatistik im Handels- und Dienstleistungsbereich," WISTA – Wirtschaft und Statistik, Statistisches Bundesamt (Destatis), Wiesbaden, vol. 74(5), pages 22-31.
    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, Polish Statistical Association, vol. 17(1), pages 25-40, March.
    8. 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.

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    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. 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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