Individual design-based prediction: the assistance from spatial relationships

Under the finite population design-based framework, spatial information regarding individuals of a population has traditionally been used for developing efficient sampling designs rather than for estimation or prediction. We propose to enhance design-based individual prediction by exploiting the spatial information derived from geography, which is a population characteristic available for each element before sampling. Individual predictors are obtained by reinterpreting deterministic interpolators under the finite population design-based framework, and their statistical properties can therefore be highlighted. We believe that this approach represents quite a novelty for spatial inference. Monte Carlo experiments help us to appreciate the performances of the proposed approach in comparison both with estimators that do not employ spatial information and with popular model-based proposals, i.e. kriging. We check whether the new predictor is suitable for inference and which are the most favourable conditions to its application. The performances of the achieved predictor are similar to those of kriging, especially for small sample sizes.