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Optimal allocation of the sample size to strata under box constraints

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Abstract

In stratified random sampling without replacement boundary conditions, such as the sample sizes within strata shall not exceed the population sizes in the respective strata, have to be considered. Stenger and Gabler (Metrika, 61:137–156, 2005) have shown a solution that satisfies upper boundaries of sample fractions within the strata. However, in modern applications one may wish to guarantee also minimal sampling fractions within strata in order to allow for reasonable separate estimations. Within this paper, an optimal allocation in the Neyman-Tschuprov sense is developed which satisfies upper and lower bounds of the sample sizes within strata. Further, a stable algorithm is given which ensures optimality. The resulting sample allocation enables users to bound design weights within stratified random sampling while considering optimality in allocation.

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Authors and Affiliations

  1. Survey Design and Methodology, GESIS - Leibniz Institute for the Social Sciences, P. O. Box 12 21 55, 68072, Mannheim, Germany

    Siegfried Gabler & Matthias Ganninger

  2. Economics and Social Statistics Department, University of Trier, FB IV, Universitätsring 15, 54296, Trier, Germany

    Ralf Münnich

Authors
  1. Siegfried Gabler
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  2. Matthias Ganninger
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  3. Ralf Münnich
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Corresponding author

Correspondence to Siegfried Gabler.

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Gabler, S., Ganninger, M. & Münnich, R. Optimal allocation of the sample size to strata under box constraints. Metrika 75, 151–161 (2012). https://doi.org/10.1007/s00184-010-0319-3

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  • DOI: https://doi.org/10.1007/s00184-010-0319-3

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