Universal Kriging and Cokriging as a Regression Procedure

Abstract

Prediction of a property on the basis of a set of point measurements in a region is required if a map of this property for the region is to be made. Of the spatial interpolation and prediction techniques, kriging is optimal among all linear procedures, as it is unbiased and has minimal variance of the prediction error. In cokriging, which has this same attractive property, additional observations of one or more covariables are used, which may lead to increased precision of the predictions. Both techniques are often applicable in different fields such as soil science, meteorology, medicine, agriculture, biology, public health, and environmental sciences (e.g., atmospheric or soil pollution). In this study we try to remove the cloud of obscurity covering the notions of kriging and cokriging by embedding them into regression procedures. This leads to a straightforward formulation of the two techniques. It turns out that kriging and cokriging differ only slightly from each other. The procedures are illustrated by two numerical examples, one to demonstrate the methodology, and one practical problem encountered in a soil study. Cokriging is found to be most valuable when a highly correlated covariable is sampled intensely.