A Kronecker-based covariance specification for spatially continuous multivariate data

We propose a covariance specification for modeling spatially continuous multivariate data. This model is based on a reformulation of Kronecker's product of covariance matrices for Gaussian random fields. The structure holds for different choices of covariance functions with parameters varying in their usual domains. In comparison with classical models from the literature, we used the Matern correlation function to specify the marginal covariances. We also assess the reparametrized generalized Wendland model as an option for efficient calculation of the Cholesky decomposition, improving the model's ability to deal with large data sets. The reduced computational time and flexible generalization for increasing number of variables, make it an attractive alternative for modelling spatially continuous data. The proposed model is fitted to a soil chemistry properties dataset, and adequacy measures, forecast errors and estimation times are compared with the ones obtained based on classical models. In addition, the model is fitted to a North African temperature dataset to illustrate the model's flexibility in dealing with large data. A simulation study is performed considering different parametric scenarios to evaluate the properties of the maximum likelihood estimators. The simple structure and reduced estimation time make the proposed model a candidate approach for multivariate analysis of spatial data.

Automated summary

This paper proposes a covariance specification for modeling spatially continuous multivariate data. The model is based on a reformulation of Kronecker's product of covariance matrices for Gaussian random fields and is applicable to different covariance functions. Compared to classical models, this model has the advantages of a simple structure, reduced estimation time, and flexible generalization.