A comparison of approaches for valid variogram achievement
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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.
KeywordsSpatial dependence Empirical variogram Valid model Fitting criteria Non-parametric estimation
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- Cressie, N. (1993),Statistics for Spatial Data, John Wiley and Sons Inc., New York.Google Scholar
- Gribov, A., Krivoruchko, K. and Ver Hoef, J. (2000), ‘Modified weighted least squares semivariogram and covariance model fitting algorithm’,Stochastic Modeling and Geostatistics. AAPG Computer Applications in Geology 2.Google Scholar
- Journel, A. and Huijbregts, C. (1978),Mining Geostatistics, Academic Press, London.Google Scholar
- Maglione, D. and Diblasi, A. (2001), ‘Choosing a valid model for the Variogram of an isotropic spatial process’,2001 Annual Conference of Int. Association for Mathematical Geology.Google Scholar
- Matheron, G. (1963), ‘Principles of geostatistics’,Economic Geology 58, 1246–1266.Google Scholar
- Ribeiro Jr, P. and Diggle, P. (2001), ‘geoR: A package for geostatistical analysis’,R-NEWS vol1, n.2, ISSN 1609–3631.Google Scholar
- Stein, M. (1998),Interpolation of Spatial Data-Some Theory for Kriging, Springer.Google Scholar