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A comparison of pivotal sampling and unequal probability sampling with replacement

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  • Chauvet, Guillaume
  • Ruiz-Gazen, Anne

Abstract

We prove that any implementation of pivotal sampling is more efficient than multinomial sampling. This yields the weak consistency of the Horvitz–Thompson estimator and the existence of a conservative variance estimator. A small simulation study supports our findings.

Suggested Citation

  • Chauvet, Guillaume & Ruiz-Gazen, Anne, 2017. "A comparison of pivotal sampling and unequal probability sampling with replacement," Statistics & Probability Letters, Elsevier, vol. 121(C), pages 1-5.
    • Handle: RePEc:eee:stapro:v:121:y:2017:i:c:p:1-5
    DOI: 10.1016/j.spl.2016.09.027
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    References listed on IDEAS

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    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. Lorenzo Fattorini & Piermaria Corona & Gherardo Chirici & Maria Chiara Pagliarella, 2015. "Design‐based strategies for sampling spatial units from regular grids with applications to forest surveys, land use, and land cover estimation," Environmetrics, John Wiley & Sons, Ltd., vol. 26(3), pages 216-228, May.
    3. 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, August.
    4. Audrey‐Anne Vallée & Bastien Ferland‐Raymond & Louis‐Paul Rivest & Yves Tillé, 2015. "Incorporating spatial and operational constraints in the sampling designs for forest inventories," Environmetrics, John Wiley & Sons, Ltd., vol. 26(8), pages 557-570, December.
    5. Roberto Benedetti & Federica Piersimoni & Paolo Postiglione, 2015. "Sampling Spatial Units for Agricultural Surveys," Advances in Spatial Science, Springer, edition 127, number 978-3-662-46008-5, december.
    6. Anton Grafström & Niklas L. P. Lundström & Lina Schelin, 2012. "Spatially Balanced Sampling through the Pivotal Method," Biometrics, The International Biometric Society, vol. 68(2), pages 514-520, June.
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    Cited by:

    1. Guillaume Chauvet & Ronan Le Gleut, 2021. "Inference under pivotal sampling: Properties, variance estimation, and application to tesselation for spatial sampling," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(1), pages 108-131, March.
    2. Roberto Benedetti & Maria Michela Dickson & Giuseppe Espa & Francesco Pantalone & Federica Piersimoni, 2022. "A simulated annealing-based algorithm for selecting balanced samples," Computational Statistics, Springer, vol. 37(1), pages 491-505, March.

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