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Efficient balanced sampling: The cube method

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  • Jean-Claude Deville
  • Yves Tille

Abstract

A balanced sampling design is defined by the property that the Horvitz--Thompson estimators of the population totals of a set of auxiliary variables equal the known totals of these variables. Therefore the variances of estimators of totals of all the variables of interest are reduced, depending on the correlations of these variables with the controlled variables. In this paper, we develop a general method, called the cube method, for selecting approximately balanced samples with equal or unequal inclusion probabilities and any number of auxiliary variables. Copyright 2004, Oxford University Press.

Suggested Citation

  • Jean-Claude Deville & Yves Tille, 2004. "Efficient balanced sampling: The cube method," Biometrika, Biometrika Trust, vol. 91(4), pages 893-912, December.
  • Handle: RePEc:oup:biomet:v:91:y:2004:i:4:p:893-912
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    File URL: http://hdl.handle.net/10.1093/biomet/91.4.893
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    Citations

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    Cited by:

    1. Maria Michela Dickson & Yves Tille', 2015. "Ordered Spatial Sampling by Means of the Traveling Salesman Problem," DEM Discussion Papers 2015/06, Department of Economics and Management.
    2. Hervé Cardot & Camelia Goga & Pauline Lardin, 2014. "Variance Estimation and Asymptotic Confidence Bands for the Mean Estimator of Sampled Functional Data with High Entropy Unequal Probability Sampling Designs," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(2), pages 516-534, June.
    3. Lennart Bondesson, 2010. "Conditional and Restricted Pareto Sampling: Two New Methods for Unequal Probability Sampling," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 37(3), pages 514-530.
    4. Maria Michela Dickson & Giuseppe Espa & Diego Giuliani, 2016. "Incomplete geocoding and spatial sampling: the effects of locational errors on population total estimation," DEM Working Papers 2016/04, Department of Economics and Management.
    5. Maria Michela Dickson & Yves Tillé, 2016. "Ordered spatial sampling by means of the traveling salesman problem," Computational Statistics, Springer, vol. 31(4), pages 1359-1372, December.
    6. Hasler, Caren & Tillé, Yves, 2014. "Fast balanced sampling for highly stratified population," Computational Statistics & Data Analysis, Elsevier, vol. 74(C), pages 81-94.
    7. Carl-Erik Särndal, 2010. "Models in Survey Sampling," Statistics in Transition new series, Główny Urząd Statystyczny (Polska), vol. 11(3), pages 539-554, December.
    8. Anton Grafström & Lina Schelin, 2014. "How to Select Representative Samples," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(2), pages 277-290, June.
    9. Arkadiusz Kozłowski, 2014. "The Use of Non- Sample Information in Exit Poll Surveys in Poland," Statistics in Transition new series, Główny Urząd Statystyczny (Polska), vol. 15(1), pages 37-58, January.
    10. repec:bla:istatr:v:85:y:2017:i:1:p:143-163 is not listed on IDEAS
    11. Tillé, Yves & Favre, Anne-Catherine, 2005. "Optimal allocation in balanced sampling," Statistics & Probability Letters, Elsevier, vol. 74(1), pages 31-37, August.
    12. Desislava Nedyalkova & Lionel Qualité & Yves Tillé, 2009. "General framework for the rotation of units in repeated survey sampling," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 63(3), pages 269-293.
    13. Yves Tillé, 2016. "The legacy of Corrado Gini in survey sampling and inequality theory," METRON, Springer;Sapienza Università di Roma, vol. 74(2), pages 167-176, August.
    14. Y. G. Berger & O. De La Riva Torres, 2016. "Empirical likelihood confidence intervals for complex sampling designs," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(2), pages 319-341, March.
    15. Kaeding, Matthias, 2016. "Fast, approximate MCMC for Bayesian analysis of large data sets: A design based approach," Ruhr Economic Papers 660, RWI - Leibniz-Institut für Wirtschaftsforschung, Ruhr-University Bochum, TU Dortmund University, University of Duisburg-Essen.
    16. repec:bla:istatr:v:85:y:2017:i:3:p:439-454 is not listed on IDEAS
    17. repec:spr:metron:v:75:y:2017:i:3:d:10.1007_s40300-017-0123-1 is not listed on IDEAS
    18. repec:kap:rqfnac:v:49:y:2017:i:2:d:10.1007_s11156-016-0596-7 is not listed on IDEAS

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