Advances in design-based spatial estimation

Under the finite population design-based framework, spatial information regarding individuals of a population has traditionally been used to develop efficient sampling designs. We aim at improving design-based estimation by exploiting the spatial information on the population elements available before sampling. Individual and global estimators are obtained by reinterpreting a deterministic interpolator under the finite population design-based framework. In this way, the randomness induced by the sampling design allows to derive the statistical properties of this estimator. We believe that this approach represents quite a novelty for spatial inference, that can be compared with already known techniques. Comparisons are performed both with estimators that do not employ spatial information but are obtained under a specific sampling design and with popular model-based proposals, i.e. kriging. A Monte Carlo experiment helped us to appreciate the performances of the proposed approach. By considering several superpopulation models we assess the effect due to different parameterizations (i.e., nugget, range and sill effects). At the same time, by varying the sampling size in the Monte Carlo experiment, we are able to evaluate the role of the sample dimension in the performances comparison. This analysis allows to figure out whether the new estimators are suitable for inference and which are the conditions favorable to their application. The results of the Monte Carlo simulation highlight that the performances of the achieved estimators are similar to kriging predictor’s especially when the sampling size is small. Finally, we observed that the use of distances represents a major boost to design-based inference.