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Optimal allocation for equal probability two-stage design

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  • Molefe Wilford

    (University of Botswana, Botswana .)

Abstract

This paper develops optimal designs when it is not feasible for every cluster to be represented in a sample as in stratified design, by assuming equal probability two-stage sampling where clusters are small areas. The paper develops allocation methods for two-stage sample surveys where small-area estimates are a priority. We seek efficient allocations where the aim is to minimize the linear combination of the mean squared errors of composite small area estimators and of an estimator of the overall mean. We suggest some alternative allocations with a view to minimizing the same objective. Several alternatives, including the area-only stratified design, are found to perform nearly as well as the optimal allocation but with better practical properties. Designs are evaluated numerically using Switzerland canton data as well as Botswana administrative districts data.

Suggested Citation

  • Molefe Wilford, 2022. "Optimal allocation for equal probability two-stage design," Statistics in Transition New Series, Polish Statistical Association, vol. 23(4), pages 129-148, December.
    • Handle: RePEc:vrs:stintr:v:23:y:2022:i:4:p:129-148:n:5
    DOI: 10.2478/stattrans-2022-0046
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    References listed on IDEAS

    as
    1. Robert G. Clark & David G. Steel, 2007. "Sampling within households in household surveys," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 170(1), pages 63-82, January.
    2. W. B. Molefe & D. K. Shangodoyin & R. G. Clark, 2015. "An approximation to the optimal subsample allocation for small areas," Statistics in Transition new series, Główny Urząd Statystyczny (Polska), vol. 16(2), pages 163-182, June.
    3. W. B. Molefe & D. K. Shangodoyin & R. G. Clark, 2015. "An Approximation To The Optimal Subsample Allocation For Small Areas," Statistics in Transition New Series, Polish Statistical Association, vol. 16(2), pages 163-182, June.
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