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Efficient balanced sampling: The cube method


  • Jean-Claude Deville
  • Yves Tille


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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    References listed on IDEAS

    1. Joel L. Horowitz, 1998. "Bootstrap Methods for Median Regression Models," Econometrica, Econometric Society, vol. 66(6), pages 1327-1352, November.
    2. Yingyao Hu & Susanne M. Schennach, 2008. "Instrumental Variable Treatment of Nonclassical Measurement Error Models," Econometrica, Econometric Society, vol. 76(1), pages 195-216, January.
    3. Wei, Ying & Carroll, Raymond J., 2009. "Quantile Regression With Measurement Error," Journal of the American Statistical Association, American Statistical Association, vol. 104(487), pages 1129-1143.
    4. Delaigle, Aurore & Hall, Peter, 2008. "Using SIMEX for Smoothing-Parameter Choice in Errors-in-Variables Problems," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 280-287, March.
    5. Hong, Han & Tamer, Elie, 2003. "A simple estimator for nonlinear error in variable models," Journal of Econometrics, Elsevier, pages 1-19.
    6. Schennach, Susanne M., 2008. "Quantile Regression With Mismeasured Covariates," Econometric Theory, Cambridge University Press, vol. 24(04), pages 1010-1043, August.
    7. Hua Liang & Suojin Wang & Raymond J. Carroll, 2007. "Partially linear models with missing response variables and error-prone covariates," Biometrika, Biometrika Trust, vol. 94(1), pages 185-198.
    8. Purdom Elizabeth & Holmes Susan P, 2005. "Error Distribution for Gene Expression Data," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 4(1), pages 1-35, July.
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    Cited by:

    1. 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.
    2. Yves Tillé, 2016. "The legacy of Corrado Gini in survey sampling and inequality theory," METRON, Springer;Sapienza Università di Roma, pages 167-176.
    3. 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.
    4. 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.
    5. Carl-Erik Särndal, 2010. "Models in Survey Sampling," Statistics in Transition new series, Główny Urząd Statystyczny (Polska), vol. 11(3), pages 539-554, December.
    6. repec:kap:rqfnac:v:49:y:2017:i:2:d:10.1007_s11156-016-0596-7 is not listed on IDEAS
    7. Andrea Fracasso & Rocco Probo, 2017. "When did inflation expectations in the Euro area de-anchor?," Applied Economics Letters, Taylor & Francis Journals, vol. 24(20), pages 1481-1485, November.
    8. Hasler, Caren & Tillé, Yves, 2014. "Fast balanced sampling for highly stratified population," Computational Statistics & Data Analysis, Elsevier, pages 81-94.
    9. Tillé, Yves & Favre, Anne-Catherine, 2005. "Optimal allocation in balanced sampling," Statistics & Probability Letters, Elsevier, pages 31-37.
    10. 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.
    11. repec:spr:metron:v:75:y:2017:i:3:d:10.1007_s40300-017-0123-1 is not listed on IDEAS

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