The problem of constructing valid parametric cross-covariance functions is challenging. We propose a simple methodology, based on latent dimensions and existing covariance models for univariate random fields, to develop flexible, interpretable and computationally feasible classes of...

Best linear unbiased prediction of spatially correlated multivariate random processes, often called cokriging in geostatistics, requires the solution of a large linear system based on the covariance and cross-covariance matrix of the observations. For many problems of practical interest, it is...

We derive a closed form expression for the likelihood function of a Gaussian max-stable process indexed by ℝ-super-d at p≤d+1 sites, d≥1. We demonstrate the gain in efficiency in the maximum composite likelihood estimators of the covariance matrix from p=2 to p=3 sites in ℝ-super-2 by means...

We derive sufficient conditions for the cross-correlation coefficient of a multivariate spatial process to vary with location when the spatial model is augmented with nugget effects. The derived class is valid for any choice of covariance functions, and yields substantial flexibility between...

There is an increasing wealth of multivariate spatial and multivariate spatio-temporal data appearing. For such data, an important part of model building is an assessment of the properties of the underlying covariance function describing variable, spatial and temporal correlations. In this...