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Unequal probability sampling from a finite population: A multicriteria approach

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  • Carrizosa, Emilio

Abstract

In this note we address the problem of determining selection probabilities for multipurpose surveys, when the aim is the simultaneous minimization of variances for each variable under study. A characterization of the set of Pareto-optimal designs is given for designs with replacement and also for a class of designs without replacement, namely, Poisson designs. As an application, we describe a problem encountered in Auditing, where both the fraction of misstatements, and the average amount of such misstatements are of interest.

Suggested Citation

  • Carrizosa, Emilio, 2010. "Unequal probability sampling from a finite population: A multicriteria approach," European Journal of Operational Research, Elsevier, vol. 201(2), pages 500-504, March.
    • Handle: RePEc:eee:ejores:v:201:y:2010:i:2:p:500-504
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    References listed on IDEAS

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    1. Carrizosa, Emilio & Romero Morales, Dolores, 2007. "A biobjective method for sample allocation in stratified sampling," European Journal of Operational Research, Elsevier, vol. 177(2), pages 1074-1089, March.
    2. Nibia Aires, 1999. "Algorithms to Find Exact Inclusion Probabilities for Conditional Poisson Sampling and Pareto πps Sampling Designs," Methodology and Computing in Applied Probability, Springer, vol. 1(4), pages 457-469, December.
    3. Lorens Imhof & Weng Kee Wong, 2000. "A Graphical Method for Finding Maximin Efficiency Designs," Biometrics, The International Biometric Society, vol. 56(1), pages 113-117, March.
    4. Matei, Alina & Tille, Yves, 2007. "Computational aspects of order [pi]ps sampling schemes," Computational Statistics & Data Analysis, Elsevier, vol. 51(8), pages 3703-3717, May.
    5. José Mayor, 2002. "Optimal cluster selection probabilities to estimate the finite population distribution function under PPS cluster sampling," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 11(1), pages 73-88, June.
    6. Valliant, Richard & Gentle, James E., 1997. "An application of mathematical programming to sample allocation," Computational Statistics & Data Analysis, Elsevier, vol. 25(3), pages 337-360, August.
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    Cited by:

    1. Carrizosa, Emilio, 2012. "On approximate Monetary Unit Sampling," European Journal of Operational Research, Elsevier, vol. 217(2), pages 479-482.

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