## 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 language | English (US) |
---|---|

Pages (from-to) | 127-137 |

Number of pages | 11 |

Journal | Mathematical Geology |

Volume | 32 |

Issue number | 1 |

DOIs | |

State | Published - 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)