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Testing the covariance structure of multivariate random fields

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  • Bo Li
  • Marc G. Genton
  • Michael Sherman

Abstract

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. Copyright 2008, Oxford University Press.

Suggested Citation

  • Bo Li & Marc G. Genton & Michael Sherman, 2008. "Testing the covariance structure of multivariate random fields," Biometrika, Biometrika Trust, vol. 95(4), pages 813-829.
    • Handle: RePEc:oup:biomet:v:95:y:2008:i:4:p:813-829
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    File URL: http://hdl.handle.net/10.1093/biomet/asn053
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    Citations

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    Cited by:

    1. Emilio Porcu & Moreno Bevilacqua & Marc G. Genton, 2016. "Spatio-Temporal Covariance and Cross-Covariance Functions of the Great Circle Distance on a Sphere," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(514), pages 888-898, April.
    2. Wang, Lili & Paul, Debashis, 2014. "Limiting spectral distribution of renormalized separable sample covariance matrices when p/n→0," Journal of Multivariate Analysis, Elsevier, vol. 126(C), pages 25-52.
    3. Claudia Cappello & Sandra De Iaco & Monica Palma, 2022. "Computational advances for spatio-temporal multivariate environmental models," Computational Statistics, Springer, vol. 37(2), pages 651-670, April.
    4. Ghulam A. Qadir & Carolina Euán & Ying Sun, 2021. "Flexible Modeling of Variable Asymmetries in Cross-Covariance Functions for Multivariate Random Fields," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 26(1), pages 1-22, March.
    5. Li, Bo & Zhang, Hao, 2011. "An approach to modeling asymmetric multivariate spatial covariance structures," Journal of Multivariate Analysis, Elsevier, vol. 102(10), pages 1445-1453, November.
    6. Marco H. Benedetti & Veronica J. Berrocal & Naveen N. Narisetty, 2022. "Identifying regions of inhomogeneities in spatial processes via an M‐RA and mixture priors," Biometrics, The International Biometric Society, vol. 78(2), pages 798-811, June.
    7. S. De Iaco & M. Palma & D. Posa, 2013. "Prediction of particle pollution through spatio-temporal multivariate geostatistical analysis: spatial special issue," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 97(2), pages 133-150, April.

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