# On Robust Estimation of Variograms in Geostatistics

• Rudolf Dutter
Chapter
Part of the Lecture Notes in Statistics book series (LNS, volume 109)

## 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.

## Key words and phrases

Geostatistics estimation of the variogram simulation robustness

## AMS 1991 subject classifications

86A32 62G35 62H11 65C05

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