A comparison of approaches for valid variogram achievement

Abstract

Variogram estimation is a major issue for statistical inference of spatially correlated random variables. Most natural empirical estimators of the variogram cannot be used for this purpose, as they do not achieve the conditional negative-definite property. Typically, this problem's resolution is split into three stages: empirical variogram estimation; valid model selection; and model fitting. To accomplish these tasks, there are several different approaches strongly defended by their authors. Our work's main purpose was to identify these approaches and compare them based on a numerical study, covering different kind of spatial dependence situations. The comparisons are based on the integrated squared errors of the resulting valid estimators. Additionally, we propose an easily implementable empirical method to compare the main features of the estimated variogram function.