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

Tatiyana V. Apanasovich, Marc Genton

Research output: Contribution to journalArticlepeer-review

115 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)15-30
Number of pages16
Issue number1
StatePublished - Mar 2010
Externally publishedYes

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledgements: The 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
This publication acknowledges KAUST support, but has no KAUST affiliated authors.


  • Asymmetry
  • Linear model of coregionalization
  • Nonseparability
  • Positive definiteness
  • Space and time
  • Stationarity

ASJC Scopus subject areas

  • Applied Mathematics
  • Agricultural and Biological Sciences (miscellaneous)
  • General Agricultural and Biological Sciences
  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • General Mathematics


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