Computational Statistics

, Volume 20, Issue 4, pp 623–642 | Cite as

A comparison of approaches for valid variogram achievement

  • Raquel Menezes
  • Pilar Garcia-Soidán
  • Manuel Febrero-Bande


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; andmodel 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.


Spatial dependence Empirical variogram Valid model Fitting criteria Non-parametric estimation 


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Copyright information

© Physica-Verlag 2005

Authors and Affiliations

  • Raquel Menezes
    • 1
  • Pilar Garcia-Soidán
    • 2
  • Manuel Febrero-Bande
    • 3
  1. 1.Department of Mathematics for Science and TechnologyUniversity of MinhoGuimarãesPortugal
  2. 2.Department of Statistics and O.R.University of VigoPontevedraSpain
  3. 3.Department of Statistics and O.R.University of Santiago de CompostelaSantiago de CompostelaSpain

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