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Design‐based properties of the nearest neighbor spatial interpolator and its bootstrap mean squared error estimator

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  • Lorenzo Fattorini
  • Marzia Marcheselli
  • Caterina Pisani
  • Luca Pratelli

Abstract

Nearest neighbor spatial interpolation for mapping continuous populations and finite populations of areas or units is approached from a design‐based perspective, that is, populations are fixed, and uncertainty stems from the sampling scheme adopted to select locations. We derive conditions for design‐based pointwise and uniform consistency of the nearest neighbor interpolators. We prove that consistency holds under certain schemes that are widely applied in environmental and forest surveys. Furthermore, we propose a pseudopopulation bootstrap estimator of the root mean squared errors of the interpolated values. Finally, a simulation study is performed to assess the theoretical results.

Suggested Citation

  • Lorenzo Fattorini & Marzia Marcheselli & Caterina Pisani & Luca Pratelli, 2022. "Design‐based properties of the nearest neighbor spatial interpolator and its bootstrap mean squared error estimator," Biometrics, The International Biometric Society, vol. 78(4), pages 1454-1463, December.
    • Handle: RePEc:bla:biomet:v:78:y:2022:i:4:p:1454-1463
    DOI: 10.1111/biom.13505
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    References listed on IDEAS

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    1. 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.
    2. L Fattorini & M Marcheselli & C Pisani & L Pratelli, 2018. "Design-based maps for continuous spatial populations," Biometrika, Biometrika Trust, vol. 105(2), pages 419-429.
    3. 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.
    4. L. Fattorini & M. Marcheselli & L. Pratelli, 2018. "Design-Based Maps for Finite Populations of Spatial Units," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(522), pages 686-697, April.
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