Spatial individual prediction under a design-based framework

In this study a non-stochastic spatial interpolator is set in the design-based finite population framework. By considering the observed locations as the result of a probabilistic sampling design, we propose a standardized weighted predictor for spatial data starting from a deterministic interpolator that does not provide uncertainty measures. The information regarding the coordinates of the spatial locations is known at the population level and is directly used in constructing the weighting system. The predictor for the individual value turns in a ratio of design-based random quantities. Its statisti- cal properties, i.e. asymptotically p-unbiasedness and p-consistency, are sketched for simple random sampling without replacement. An application to an environmental dataset is presented, in order to appreciate predictor performances in correspondence of different sampling fractions.