Computational Statistics
http://comst.wiwi.hu-berlin.de/

Abstract Volume 20 Issue 4 (2005) pp 623-642

A comparison of approaches for valid variogram achievement

Raquel Menezes¹, Pilar Garcia-Soidán² and Manuel Febrero-Bande³

¹Department of Mathematics for Science and Technology, University of Minho, 4800-058 Guimarães, Portugal.

²Department of Statistics and O.R., University of Vigo, Campus A Xunqueira, Pontevedra 36005, Spain.

³Department of Statistics and O.R., University of Santiago de Compostela, Campus Sur, Santiago de Compostela 15771, Spain.

Summary

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.

Keywords:Spatial dependence, Empirical variogram, Valid model, Fitting criteria, Non-parametric estimation.

Article not available online