Cross-covariance functions for multivariate random fields based on latent dimensions
AbstractThe 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 cross-covariance functions in closed form. We focus on spatio-temporal cross-covariance functions that can be nonseparable, asymmetric and can have different covariance structures, for instance different smoothness parameters, in each component. We discuss estimation of these models and perform a small simulation study to demonstrate our approach. We illustrate our methodology on a trivariate spatio-temporal pollution dataset from California and demonstrate that our cross-covariance performs better than other competing models. © 2010 Biometrika Trust.
CitationApanasovich TV, Genton MG (2010) Cross-covariance functions for multivariate random fields based on latent dimensions. Biometrika 97: 15–30. Available: http://dx.doi.org/10.1093/biomet/asp078.
SponsorsThe authors are grateful to the editor, an associate editor and two anonymous referees for theirvaluable comments. This research was sponsored by the National Science Foundation, U.S.A.,and by an award made by the King Abdullah University of Science and Technology
PublisherOxford University Press (OUP)