Spatial statistics of clustered data

Abstract

Modern spatial statistics techniques are widely used to make predictions for natural processes that are continuously distributed over some convex domain. Implementation of these techniques often relies on the adequate estimation of certain spatial correlation functions such as the covariance and the variogram from the data sets available. This work studies the practical estimation of such spatial correlation functions in the case of clustered data. The coefficient of variation of the dimensionless spatial density of the point pattern of sample locations is suggested as a useful metric for degree of clusteredness of the clustered data set. We show that the common variogram estimator becomes increasingly unreliable with increasing coefficient of variation of the dimensionless spatial density of the point pattern of sample locations. Moreover, we present a modified form of the variogram estimator that incorporates declustering weights, and propose a scheme for estimating the declustering weights based on zones of proximity. Finally, insight is gained in terms of a numerical application of the common and modified methods on piezometric head data collected over an irregular network.