THE 2ND-ORDER STATIONARY UNIVERSAL KRIGING MODEL REVISITED

Universal kriging originally was developed for problems of spatial int erpolation if a drift seemed to be justified to model the experimental data. Bur its use has been questioned in relation to the bins of the estimated underlying variogram (variogram of the residuals), and furth ermore universal kriging came to be considered on old-fashioned method after the theory of intrinsic random functions was developed. In this paper the model is reexamined together with methods for handling prob lems in the inference of parameters. The efficiency of the inference o f covariance parameters is shown in terms of bias, variance, and mean square error of the sampling distribution obtained by Monte Carlo simu lation for three different estimators (maximum likelihood, bias correc ted maximum likelihood, and restricted maximum likelihood). ii is show n that unbiased estimates for the covariance parameters may be obtaine d but if the number of samples is small there can be no guarantee of ' good' estimates (estimates close to the true value) because the sampli ng variance usually is large. This problem is not specific to the univ ersal kriging model but rather arises in any model where parameters ar e inferred from experimental data. The validity of the estimates may b e evaluated statistically as a risk function as is shown in this paper .