Estimating covariance functions of multivariate skew-Gaussian random fields on the sphere

This paper considers a multivariate spatial random field, with each component having univariate marginal distributions of the skew-Gaussian type. We assume that the field is defined spatially on the unit sphere embedded in R3, allowing for modeling data available over large portions of planet Earth. This model admits explicit expressions for the marginal and cross covariances. However, the n-dimensional distributions of the field are difficult to evaluate, because it requires the sum of 2n terms involving the cumulative and probability density functions of a n-dimensional Gaussian distribution. Since in this case inference based on the full likelihood is computationally unfeasible, we propose a composite likelihood approach based on pairs of spatial observations. This last being possible thanks to the fact that we have a closed form expression for the bivariate distribution. We illustrate the effectiveness of the method through simulation experiments and the analysis of a real data set of minimum and maximum surface air temperatures.