Mathematical Geology

, Volume 32, Issue 1, pp 127–137

The Correlation Structure of Matheron's Classical Variogram Estimator Under Elliptically Contoured Distributions

  • Marc G. Genton

DOI: 10.1023/A:1007511019496

Cite this article as:
Genton, M.G. Mathematical Geology (2000) 32: 127. doi:10.1023/A:1007511019496


The classical variogram estimator proposed by Matheron can be written as a quadratic form of the observations. When data have an elliptically contoured distribution with constant mean, the correlation between the classical variogram estimator at two different lags is a function of the spatial design matrix, the covariance matrix, and the kurtosis. Several specific cases are studied closely. A subclass of elliptically contoured distributions with a particular family of covariance matrices is shown to possess exactly the same correlation structure for the classical variogram estimator as the multivariate independent Gaussian distribution. The consequences on variogram fitting by generalized least squares are discussed.

variogram estimationquadratic formkurtosisvariogram fittinggeneralized least squares

Copyright information

© International Association for Mathematical Geology 2000

Authors and Affiliations

  • Marc G. Genton
    • 1
  1. 1.Department of MathematicsMassachusetts Institute of TechnologyCambridgeUSA