A pairwise likelihood approach for the empirical estimation of the underlyingvariograms in the plurigaussian models

The plurigaussian model is particularly suited to describe categorical regionalized variables. Starting from a simple principle, the thresh-olding of one or several Gaussian random fields (GRFs) to obtain categories, the plurigaussian model is well adapted for a wide range ofsituations. By acting on the form of the thresholding rule and/or the threshold values (which can vary along space) and the variograms ofthe underlying GRFs, one can generate many spatial configurations for the categorical variables. One difficulty is to choose variogrammodel for the underlying GRFs. Indeed, these latter are hidden by the truncation and we only observe the simple and cross-variogramsof the category indicators. In this paper, we propose a semiparametric method based on the pairwise likelihood to estimate the empiricalvariogram of the GRFs. It provides an exploratory tool in order to choose a suitable model for each GRF and later to estimate its param-eters. We illustrate the efficiency of the method with a Monte-Carlo simulation study .The method presented in this paper is implemented in the R packageRGeostats.