Abstract
The distribution of regionalized variables in the field of spatial statistics is mainly characterized by the variogram (or the covariance-function), which essentially is the variance of the differences of the variables in space. The usual estimate (empirical variance) of this function is highly non-robust.
Several alternative (robust) proposals for the estimation can be found in the literature. The definition often does not follow an obvious intuition (e.g., the estimator of Cressie and Hawkins). The present paper considers different estimators of the variogram (including the application of very new scale estimators). The investigation is mainly done by simulation in the one-dimensional case: data on regular and irregular grids. The results are rather surprising. The behavior of the estimators sometimes is unexpected. The main reasons seem to be the high dependence between the data values and the small sample size if the spatial distribution is irregular, both, however, correspond to practical situations often met.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Cressie, N. and Hawkins, D.M. (1980): Robust estimation of the variogram. Math. Geol. 12(2) 115–125.
Croux, C. and Rousseeuw, P.J. (1992): Time-efficient algorithms for two highly robust estimators of scale. In Computational Statistics (Y. Dodge and J. Whittaker, eds.), Vol. 1, 411–428. Physica-Verlag, Heidelberg.
Dowd, P.A. (1984): The variogram and kriging: Robust and resistent estimators. In Geostatistics for Natural Resource Characterization (G. Verly et al., eds.), 91–106. D. Reidel, Dordrecht.
Dutter, R. (1985): Geostatistik. Eine Einführung mit Anwendungen. B.G. Teubner, Stuttgart.
Harmacek, P. (1992): Geostatistics: Robust Estimation for the Semivariogram — A Simulation Study. Master’s Thesis, Inst. f. Statistik u. Wahrscheinlichkeitstheorie, Technical University, Vienna. In German.
Journel, A.G. and Huijbregts, Ch.J. (1978): Mining Geostatistics. Academic Press, New York.
Matheron, G. (1971): The Theory of Regionalized Variables and Its Applications. Les Cahiers du Centre de Morphologie Mathématique de Paris, Fontainebleau, Frankreich.
Rousseeuw, P.J. (1983): Multivariate estimation with high breakdown point. In Mathematical Statistics and Applications Fourth Pannonian Symposium on Mathematical Statistics and Probability, Bad Tatzmannsdorf, Austria, September 4–10, 1983 (I. Vincze, W. Grossmann, G. Pflug and W. Wertz, eds.), Vol. B, 283–297, Budapest, 1985. Akadémiai Kiadó.
Rousseeuw, P.J. and Croux, C. (1991): Alternatives to the median absolute deviation. Technical Report 91-43, Universitaire Instelling Antwerpen, Antwerpen, Belgium.
Rousseeuw, P.J. and Croux, C. (1993). Alternatives to the median absolute deviation. J. Amer. Statist. Assoc. 88(424) 1273–1283.
Rousseeuw, P.J. and Leroy, A.M. (1987): Robust Regression and Outlier Detection. John Wiley, New York.
Wurzer, F. (1990): Geostatistics: Exploratory, Resistant, and Robust Approaches. Ph.D. Thesis, Technical University, Vienna.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1996 Springer-Verlag New York, Inc.
About this chapter
Cite this chapter
Dutter, R. (1996). On Robust Estimation of Variograms in Geostatistics. In: Rieder, H. (eds) Robust Statistics, Data Analysis, and Computer Intensive Methods. Lecture Notes in Statistics, vol 109. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-2380-1_10
Download citation
DOI: https://doi.org/10.1007/978-1-4612-2380-1_10
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-94660-3
Online ISBN: 978-1-4612-2380-1
eBook Packages: Springer Book Archive