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Estimation of a proportion in survey sampling using the logratio approach

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  • Karel Hron

  • Matthias Templ

  • Peter Filzmoser

Abstract

The estimation of a mean of a proportion is a frequent task in statistical survey analysis, and often such ratios are estimated from compositions such as income components, wage components, tax components, etc. In practice, the weighted arithmetic mean is regularly used to estimate the center of the data. However, this estimator is not appropriate if the ratios are estimated from compositions, because the sample space of compositional data is the simplex and not the usual Euclidean space. We demonstrate that the weighted geometric mean is useful for this purpose. Even for different sampling designs, the weighted geometric mean shows excellent behavior. Copyright Springer-Verlag Berlin Heidelberg 2013

Suggested Citation

  • Karel Hron & Matthias Templ & Peter Filzmoser, 2013. "Estimation of a proportion in survey sampling using the logratio approach," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 76(6), pages 799-818, August.
    • Handle: RePEc:spr:metrik:v:76:y:2013:i:6:p:799-818
    DOI: 10.1007/s00184-012-0416-6
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    References listed on IDEAS

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    1. Tony Atkinson & Bea Cantillon & Eric Marlier & Brian Nolan, 2002. "Indicators for Social Inclusion," Politica economica, Società editrice il Mulino, issue 1, pages 7-28.
    2. Phillip S. Kott & Yan K. Liu, 2009. "One‐Sided Coverage Intervals for a Proportion Estimated from a Stratified Simple Random Sample," International Statistical Review, International Statistical Institute, vol. 77(2), pages 251-265, August.
    3. Atkinson, Tony & Cantillon, Bea & Marlier, Eric & Nolan, Brian, 2002. "Social Indicators: The EU and Social Inclusion," OUP Catalogue, Oxford University Press, number 9780199253494.
    4. Karel Hron & Lubomír Kubáček, 2011. "Statistical properties of the total variation estimator for compositional data," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 74(2), pages 221-230, September.
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