Assessing spatial dependence for clustered data

Abstract

Variogram analysis provides a useful tool for measuring the dependence between spatial locations. Suppose that the nature of the sampling process leads to the presence of clustered data; the latter makes it advisable to use a variogram estimator that aims to adjust for clustering of samples. In this setting, the use of a nonparametric weighted estimator, obtained by considering an inverse weight to the neighborhood density combined with the kernel method, seems to have a satisfactory behavior in practice. Thus, we proceed in this work with the theoretical study of the latter estimator, by proving that it is asymptotically unbiased as well as consistent and by providing criteria for selection of the bandwidth parameter and the neighborhood radius.