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

Tatiyana V. Apanasovich, Marc Genton

Research output: Contribution to journalArticlepeer-review

114 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


  • 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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