Estimation in random fields with scattered data

The design of linear minimum variance unbiased estimates in 2-D random fields (RF) is a standard problem when the mean and the covariance function of the field are known. Here, we investigate the case where the data are so scarce and so scattered in space that reliable estimates of the covariance function are impossible to obtain by classical procedures. Using the variogram of the RF rather than the covariance function, we develop a procedure for the estimation of a variogram model, which then leads to meaningful estimates of various functionals of the RF.