Individual spatial prediction under the design-based framework

Spatial inference is usually carried out by means of model-based techniques, which estimate the underlying superpopulation model generating the data. However, at present, design-based methods for inference on spatial data are being rediscovered, even if the related techniques are mostly used for estimating synthetic population values, i.e. means and totals. The aim of this work is to develop a class of design-based individual spatial predictors able to exploit the spatial information available before sampling. Such predictors are able to replicate the observed values when the spatial location is sampled and otherwise predict unobserved values through weighted sums as is usual in spatial interpolation. The weights are constructed in order to assign higher influence to the observations close to the location to predict and fade away as the spatial lag increases. Moreover, as is customary, they are built in order to sum to one in the sample, needing a standardization that induces ratios of random variables. Therefore, their statistical properties can be assessed only in approximate way. Then, among all possible, an individual design-based predictor is compared with the kriging predictor through a Monte Carlo simulation showing that, especially at small sampling dimensions, its properties are quite similar to the kriging’s.