Likelihood analysis for a class of spatial geostatistical compositional models

We propose a model-based geostatistical approach to deal with regionalized compositions. We combine the additive-log-ratio transformation with multivariate geostatistical models whose covariance matrix is adapted to take into account the correlation induced by the compositional structure. Such specification allows the usage of standard likelihood methods for parameters estimation. For spatial prediction we combined a back-transformation with the Gauss-Hermite method to approximate the conditional expectation of the compositions. We analyze particle size fractions of the top layer of a soil for agronomic purposes which are typically expressed as proportions of sand, clay and silt. Additionally a simulation study assess the small sample properties of the maximum likelihood estimator.