Random perturbation methods applied to multivariate spatial sampling design

The problem of estimating a multivariate spatial random process from observations obtained by sampling a related multivariate spatial random process is considered. A method based on additive perturbation of the variables of interest is proposed for the assignment of degrees of relative importance to the variables and/or locations of interest in the design of sampling strategies. In the case where the variables involved have a multivariate Gaussian distribution, some theoretical results are provided to justify the method proposed; in particular, it is proved that the amount of information contained in the data on the perturbed variables of interest is never higher than that contained in the original variables of interest. These results and the application of the method are illustrated with an empirical study, showing the variation of the effects of perturbation on spatial sampling design configurations and related ratios of information for different degrees of dependence according to the model specifications. Copyright (C) 2001 John Wiley & Sons, Ltd.