Residual Diagnostics for Variogram Fitting

• Activity Number: 308
• Type: Contributed
• Date/Time: Wednesday, August 14, 2002 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistics & the Environment*
• Author(s): Werner Mueller*+ and Ernst Glatzer
• Affiliation(s): Vienna University of Economics and Austrian Central Bank
• Keywords: generalized least squares ; spatial data ; leave-one-out residuals ; variogram cloud ; geostatistics

Abstract

The variogram cloud is increasingly employed in geostatistics, both as an exploratory tool--see Ploner (1999)--as well as for variogram fitting--cf. Mueller (1999). Unfortunately, in its pure form the variogram cloud cannot be effectively used to assess the fit of a corresponding variogram model. This is due to the fact that its entries are highly correlated and heteroscedastic (and possibly distorted by anisotropy). We propose fitting of a model by GLS and suggest some diagnostics for assessing the fit based on diagnostics found in the literature for GLS fitting--e.g,. Haslett and Hayes (1998). The presented diagnostics are applied to an example data set of chlorid concentrations in the Suedliche Tullnerfeld, Austria.

References: Haslett, J. and Hayes, K. (1998) "Residuals for the linear model with general covariance structure," J. R. Statist. Soc. B, 60, 201-215.

Mueller, W.G. (1999) "Least-squares fitting from the variogram cloud," Statistics & Probability Letters, 43, 93-98.

Ploner, A. (1999) "The use of the variogram cloud in geostatistical modelling," Environmetrics, 10, 413-437.