Cross-covariance functions for multivariate random fields based on latent dimensions

T. V. Apanasovich, M. G. Genton

Research output: Contribution to journalArticlepeer-review

91 Scopus citations

Abstract

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 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.
Original languageEnglish (US)
Pages (from-to)15-30
Number of pages16
JournalBiometrika
Volume97
Issue number1
DOIs
StatePublished - Feb 16 2010
Externally publishedYes

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