We analyse the estimation of the 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 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.

Fattorini, L., Marcheselli, M., Pisani, C., Pratelli, L. (2018). Design-based maps for continuous spatial populations. BIOMETRIKA, 105(2), 419-429 [10.1093/biomet/asy012].

Design-based maps for continuous spatial populations

L. FATTORINI;M. MARCHESELLI;C. PISANI;
2018-01-01

Abstract

We analyse the estimation of the 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 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.
2018
Fattorini, L., Marcheselli, M., Pisani, C., Pratelli, L. (2018). Design-based maps for continuous spatial populations. BIOMETRIKA, 105(2), 419-429 [10.1093/biomet/asy012].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11365/1032910