We now examine some other best linear unbiased estimators, including estimation with given mean or drift, estimation of the drift coefficients, estimation of the continuous part of a regionalized variable with a nugget, and estimation of spatial averages or volumes. Many of the formulae appearing in this chapter are summarized in reference [84].

Overview

So far we have seen how to apply best linear unbiased estimation (BLUE) when we have n observations z(x1),…, z(xn) and we want to find the value of z at location x0, with z(x) being modeled as an intrinsic process. The method is known as ordinary kriging or just kriging. We also studied the same problem when the mean is variable, consisting of the summation of terms, each of which having one unknown drift coefficient; the approach that resulted is known as universal kriging.

By slightly changing the criteria or the conditions, variants of these estimators can be obtained. Furthermore, one can solve other problems; for example, one can estimate the volume or the spatial average of z(x) over a certain domain or one can estimate the slope of z(x) in a certain direction at some point [110]. There is no end to the list of problems in which we can apply estimation techniques.

In all of these cases, we apply best linear unbiased estimation. Once we set up the problem, this methodology is mathematically and algorithmically straightforward. In other words, we always follow the same basic steps and we always end up with a system of linear equations that can be solved with relatively little effort with currently available computers.