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Linear Assignment Sampling: Spatially Balanced Sampling With Auxiliary Variables

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  • B. L. Robertson
  • C. J. Price
  • M. Reale

Abstract

Estimating parameters of spatial populations requires a sample of response values distributed over the study region. When spatial trends are present, spatially balanced designs give more precise results for commonly used estimators. If auxiliary variables are available, these can also be included in the design to improve precision further. This article proposes a new spatially balanced design to force sample spread in the space of the auxiliary variables. All we require is a distance measure between population units. Numerical results show that the method generates spatially balanced samples and compares favorably with existing designs. We provide two example applications using spatial populations with auxiliary variables and consider equal and unequal probability designs.

Suggested Citation

  • B. L. Robertson & C. J. Price & M. Reale, 2025. "Linear Assignment Sampling: Spatially Balanced Sampling With Auxiliary Variables," Environmetrics, John Wiley & Sons, Ltd., vol. 36(7), October.
    • Handle: RePEc:wly:envmet:v:36:y:2025:i:7:n:e70042
    DOI: 10.1002/env.70042
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    References listed on IDEAS

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    1. 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.
    2. 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.
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