Testing the covariance structure of multivariate random fields

Bo Li*, Marc Genton, Michael Sherman

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

52 Scopus citations


There is an increasing wealth of multivariate spatial and multivariate spatio-temporal data appearing. For such data, an important part of model building is an assessment of the properties of the underlying covariance function describing variable, spatial and temporal correlations. In this paper, we propose a methodology to evaluate the appropriateness of several types of common assumptions on multivariate covariance functions in the spatio-temporal context. The methodology is based on the asymptotic joint normality of the sample space-time cross-covariance estimators. Specifically, we address the assumptions of symmetry, separability and linear models of coregionalization. We conduct simulation experiments to evaluate the sizes and powers of our tests and illustrate our methodology on a trivariate spatio-temporal dataset of pollutants over California.

Original languageEnglish (US)
Pages (from-to)813-829
Number of pages17
Issue number4
StatePublished - Dec 1 2008


  • Covariance
  • Linear model of coregionalization
  • Separability
  • Space and time
  • Symmetry

ASJC Scopus subject areas

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


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