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Design-based maps for continuous spatial populations

Author

Listed:
  • L Fattorini
  • M Marcheselli
  • C Pisani
  • L Pratelli

Abstract

SUMMARYWe analyse the estimation of values of a survey variable throughout a continuum of points in a study area when a sample of points is selected by a probabilistic sampling scheme. At each point, the value is estimated using an inverse distance weighting interpolator, and maps of the survey variable can be obtained. We investigate the design-based asymptotic properties of the interpolator when the study area remains fixed and the number of sampled points approaches infinity, and we derive conditions ensuring design-based asymptotic unbiasedness and consistency. The conditions essentially require the existence of a pointwise or uniformly continuous function describing the behaviour of the survey variable and the use of spatially balanced designs to select points. Finally, we propose a computationally simple mean squared error estimator.

Suggested Citation

  • 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.
    • Handle: RePEc:oup:biomet:v:105:y:2018:i:2:p:419-429.
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    File URL: http://hdl.handle.net/10.1093/biomet/asy012
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    Cited by:

    1. 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.

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