Reducing fluctuations in the sample variogram

Abstract

In the analysis of regionalized data, irregular sampling patterns are often responsible for large deviations (fluctuations) between the theoretical and sample semi-variograms. This article proposes a new semi-variogram estimator that is unbiased irrespective of the actual multivariate distribution of the data (provided an assumption of stationarity) and has the minimal variance under a given multivariate distribution model. Such an estimator considerably reduces fluctuations in the sample semi-variogram when the data are strongly correlated and clustered in space, and proves to be robust to a misspecification of the multivariate distribution model. The traditional and proposed semi-variogram estimators are compared through an application to a pollution dataset.