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One point per cluster spatially balanced sampling

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  • Robertson, Blair
  • Price, Chris

Abstract

A spatial sampling design determines where sample locations are placed in a study area so that population parameters can be estimated with relatively high precision. Spatially balanced designs have good spatial spread and give precise results for commonly used estimators when surveying natural resources. A new design is proposed which draws spatially balanced samples from stratified and unstratified populations. The method is two-fold. First, the population is partitioned into n compact geographic clusters. Then, a one point per cluster sample is drawn using a linear assignment strategy that optimises the spatial spread of the sample. Numerical results on several simulated populations show that the method generates well-spread samples and compares favourably with existing designs. An example application is also provided, where soil organic matter concentrations are estimated over a study area in Voorst, Netherlands.

Suggested Citation

  • Robertson, Blair & Price, Chris, 2024. "One point per cluster spatially balanced sampling," Computational Statistics & Data Analysis, Elsevier, vol. 191(C).
    • Handle: RePEc:eee:csdana:v:191:y:2024:i:c:s0167947323001998
    DOI: 10.1016/j.csda.2023.107888
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    References listed on IDEAS

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    1. Borgwardt, S. & Brieden, A. & Gritzmann, P., 2017. "An LP-based k-means algorithm for balancing weighted point sets," European Journal of Operational Research, Elsevier, vol. 263(2), pages 349-355.
    2. Anton Grafström & Alina Matei, 2018. "Spatially Balanced Sampling of Continuous Populations," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 45(3), pages 792-805, September.
    3. B. L. Robertson & J. A. Brown & T. McDonald & P. Jaksons, 2013. "BAS: Balanced Acceptance Sampling of Natural Resources," Biometrics, The International Biometric Society, vol. 69(3), pages 776-784, September.
    4. Robertson, B.L. & Reale, M. & Price, C.J. & Brown, J.A., 2021. "Quasi-random ranked set sampling," Statistics & Probability Letters, Elsevier, vol. 171(C).
    5. 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.
    6. 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.
    7. Anton Grafström & Yves Tillé, 2013. "Doubly balanced spatial sampling with spreading and restitution of auxiliary totals," Environmetrics, John Wiley & Sons, Ltd., vol. 24(2), pages 120-131, March.
    8. Robertson, B.L. & McDonald, T. & Price, C.J. & Brown, J.A., 2017. "A modification of balanced acceptance sampling," Statistics & Probability Letters, Elsevier, vol. 129(C), pages 107-112.
    9. B. L. Robertson & O. Ozturk & O. Kravchuk & J. A. Brown, 2022. "Spatially Balanced Sampling with Local Ranking," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 27(4), pages 622-639, December.
    10. 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.
    11. B. L. Robertson & O. Ozturk & O. Kravchuk & J. A. Brown, 2022. "Correction to: Spatially Balanced Sampling with Local Ranking," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 27(4), pages 640-640, December.
    12. R. Benedetti & F. Piersimoni & P. Postiglione, 2017. "Alternative and complementary approaches to spatially balanced samples," METRON, Springer;Sapienza Università di Roma, vol. 75(3), pages 249-264, December.
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