Spatial declustering weights

Abstract

Because of autocorrelation and spatial clustering, all data within a given dataset have not the same statistical weight for estimation of global statistics such mean, variance, or quantiles of the population distribution. A measure of redundancy (or nonredundancy) of any given regionalized random variable Z(u_α)within any given set (of size N) of random variables is proposed. It is defined as the ratio of the determinant of the N X Ncorrelation matrix to the determinant of the (N - 1) X (N - 1)correlation matrix excluding random variable Z(u_α).This ratio measures the increase in redundancy when adding the random variable Z(u_α)to the (N - 1 )remainder. It can be used as declustering weight for any outcome (datum) z(u_α). When the redundancy matrix is a kriging covariance matrix, the proposed ratio is the crossvalidation simple kriging variance. The covariance of the uniform scores of the clustered data is proposed as a redundancy measure robust with respect to data clustering.