Constructing and fitting models for cokriging and multivariable spatial prediction

Abstract

We consider best linear unbiased prediction for multivariable data. Minimizing mean-squared-prediction errors leads to prediction equations involving either covariances or variograms. We discuss problems with multivariate extensions that include the construction of valid models and the estimation of their parameters. In this paper, we develop new methods to construct valid crossvariograms, fit them to data, and then use them for multivariable spatial prediction, including cokriging. Crossvariograms are constructed by explicitly modeling spatial data as moving averages over white noise random processes. Parameters of the moving average functions may be inferred from the variogram, and with few additional parameters, crossvariogram models are constructed. Weighted least squares is then used to fit the crossvariogram model to the empirical crossvariogram for the data. We demonstrate the method for simulated data, and show a considerable advantage of cokriging over ordinary kriging. © 1998 Elsevier Science B.V. All rights reserved.