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Spatial Spread Sampling Using Weakly Associated Vectors

Author

Listed:
  • Raphaël Jauslin

    (University of Neuchatel)

  • Yves Tillé

    (University of Neuchatel)

Abstract

Geographical data are generally autocorrelated. In this case, it is preferable to select spread units. In this paper, we propose a new method for selecting well-spread samples from a finite spatial population with equal or unequal inclusion probabilities. The proposed method is based on the definition of a spatial structure by using a stratification matrix. Our method exactly satisfies given inclusion probabilities and provides samples that are very well spread. A set of simulations shows that our method outperforms other existing methods such as the generalized random tessellation stratified or the local pivotal method. Analysis of the variance on a real dataset shows that our method is more accurate than these two. Furthermore, a variance estimator is proposed.

Suggested Citation

  • Raphaël Jauslin & Yves Tillé, 2020. "Spatial Spread Sampling Using Weakly Associated Vectors," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 25(3), pages 431-451, September.
    • Handle: RePEc:spr:jagbes:v:25:y:2020:i:3:d:10.1007_s13253-020-00407-1
    DOI: 10.1007/s13253-020-00407-1
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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. Eddelbuettel, Dirk & Sanderson, Conrad, 2014. "RcppArmadillo: Accelerating R with high-performance C++ linear algebra," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 1054-1063.
    3. 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.
    4. 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.
    5. 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.
    6. Peter J. Diggle & Raquel Menezes & Ting‐li Su, 2010. "Geostatistical inference under preferential sampling," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 59(2), pages 191-232, March.
    7. Jean-Claude Deville & Yves Tille, 2004. "Efficient balanced sampling: The cube method," Biometrika, Biometrika Trust, vol. 91(4), pages 893-912, December.
    8. Stevens, Don L. & Olsen, Anthony R., 2004. "Spatially Balanced Sampling of Natural Resources," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 262-278, January.
    9. Roberto Benedetti & Federica Piersimoni & Paolo Postiglione, 2017. "Spatially Balanced Sampling: A Review and A Reappraisal," International Statistical Review, International Statistical Institute, vol. 85(3), pages 439-454, December.
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    Cited by:

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    3. G. Alleva & G. Arbia & P. D. Falorsi & V. Nardelli & A. Zuliani, 2023. "Optimal two-stage spatial sampling design for estimating critical parameters of SARS-CoV-2 epidemic: Efficiency versus feasibility," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 32(3), pages 983-999, September.
    4. Rosa Maria Di Biase & Lorenzo Fattorini & Sara Franceschi & Mirko Grotti & Nicola Puletti & Piermaria Corona, 2022. "From model selection to maps: A completely design‐based data‐driven inference for mapping forest resources," Environmetrics, John Wiley & Sons, Ltd., vol. 33(7), November.
    5. Raphaël Jauslin & Bardia Panahbehagh & Yves Tillé, 2022. "Sequential spatially balanced sampling," Environmetrics, John Wiley & Sons, Ltd., vol. 33(8), December.

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