On the automatic inference and modelling of a set of indicator covariances and cross-covariances

Abstract

The indicator approach to estimating spatial, local cumulative distributions is a well-known, non-parametric alternative to classical linear (ordinary kriging) and nonlinear (disjunctive kriging) geostatistics approaches. The advantages of the method are that it is distribution-free and non-parametric, is capable of dealing with data with very skewed distributions, provides a complete solution to the estimation problem and accounts for high connectivity of extreme values. The main drawback associated with the procedure is the amount of inference required. For example, if the distribution function is defined by 15 discrete thresholds, then 15 indicator covariances and 105 indicator cross-covariances must be estimated and models fitted. Simplifications, such as median indicator kriging, have been introduced to address this problem rather than using the theoretically preferable indicator cokriging. In this paper we propose a method in which the inference and modelling of a complete set of indicator covariances and cross-covariances is done automatically in an efficient and flexible manner. The inference is simplified by using relationships derived for indicators in which the indicator cross-covariances are written in terms of the direct indicator covariances. The procedure has been implemented in a public domain computer program the use of which is illustrated by a case study. This technique facilitates the use of the full indicator approach instead of the various simplified alternatives.