The correlation structure of Matheron's classical variogram estimator under elliptically contoured distributions

Marc Genton*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

8 Scopus citations

Abstract

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.

Original languageEnglish (US)
Pages (from-to)127-137
Number of pages11
JournalMathematical Geology
Volume32
Issue number1
DOIs
StatePublished - Jan 1 2000

Keywords

  • Generalized least squares
  • Kurtosis
  • Quadratic form
  • Variogram estimation
  • Variogram fitting

ASJC Scopus subject areas

  • Mathematics (miscellaneous)
  • Earth and Planetary Sciences (miscellaneous)

Fingerprint Dive into the research topics of 'The correlation structure of Matheron's classical variogram estimator under elliptically contoured distributions'. Together they form a unique fingerprint.

Cite this