On the Automatic Inference and Modelling of a Set of Indicator Covariances and Cross-Covariances

Abstract

The indicator approach to estimating spatial, local cumulativedistributions is a well-known, non-parametric alternative to classicallinear (ordinary kriging) and nonlinear (disjunctive kriging)geostatistics approaches. The advantages of the method are that it isdistribution-free and non-parametric, is capable of dealing with datawith very skewed distributions, provides a complete solution to theestimation problem and accounts for high connectivity of extreme values.The main drawback associated with the procedure is the amount ofinference required. For example, if the distribution function is definedby 15 discrete thresholds, then 15 indicator covariances and 105indicator cross-covariances must be estimated and models fitted.Simplifications, such as median indicator kriging, have been introducedto address this problem rather than using the theoretically preferableindicator colcriging. In this paper we propose a method in which theinference and modelling of a complete set of indicator covariances andcross-covariances is done automatically in an efficient and flexiblemanner. The inference is simplified by using relationships derived forindicators in which the indicator cross-covariances are written in termsof the direct indicator covariances. The procedure has been implementedin a public domain computer program the use of which is illustrated by acase study. This technique facilitates the use of the full indicatorapproach instead of the various simplified alternatives.