Comparison of approaches to spatial estimation in a bivariate context

The problem of estimating a regionalized variable in the presence of other secondary variables is encountered in spatial investigations. Given a context in which the secondary variable is known everywhere (or can be estimated with great precision), different estimation methods are compared: regression, regression with residual simple kriging, kriging, simple kriging with a mean obtained by regression, kriging with an external drift, and cokriging. The study focuses on 19 pairs of regionalized variables from five different datasets representing different domains (geochemical, environmental, geotechnical). The methods are compared by cross-validation using the mean absolute error as criterion. For correlations between the principal and secondary variable under 0.4, similar results are obtained using kriging and cokriging, and these methods are superior slightly to the other approaches in terms of minimizing estimation error. For correlations greater than 0.4, cokriging generally performs better than other methods, with a reduction in mean absolute errors that can reach 46% when there is a high degree of correlation between the variables. Kriging with an external drift or kriging the residuals of a regression (SKR) are almost as precise as cokriging.