Design-based maps for continuous spatial populations

L Fattorini, M Marcheselli, C Pisani and L Pratelli

Biometrika, 2018, vol. 105, issue 2, 419-429

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.

Keywords: Design consistency; Sampling; Spatial interpolation (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (1)

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