Spatial Network Sampling in Small Area Estimation

The spatial distribution of a population represents an important in sampling designs where that use the network of the contiguities between units as auxiliary information in the frame. Its use is increased in the last decades as the GIS and GPS technologies made more and more cheap to add information regarding the exact or estimated position for each record in the frame. These data may represent a source of auxiliaries that can be helpful to design effective sampling strategies, which, assuming that the observed phenomenon is related with the spatial features of the population, could gather a considerable gain in their efficiency by a proper use of this particular information. This assumption is particularly relevant if we are dealing with not planned geographical domains or, in other terms, if we want that the design will be efficient for a future use within a small area estimation context. A method for selecting samples from a spatial finite population that are well spread over the population in every dimension should guarantee that the variability of the expected sampling ratio should be smaller than that obtained by using a simple random sampling. Some algorithms of sample selection are presented such that a set of units with higher within distance will be selected with higher probability than a set of nearby units. Some examples on real data show that the RMSE of the EBLUP estimates applied to samples selected with these network methods are lower than those obtained by using a classical solution as the Generalized Random Tessellation Stratified (GRTS). The proposed algorithm, even if in its nature it is computationally intensive, seems to be a feasible solution even when dealing with frames relevant to large finite network populations.