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Characterization theorems for some classes of covariance functions associated to vector valued random fields

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  • Porcu, Emilio
  • Zastavnyi, Viktor

Abstract

We characterize some important classes of cross-covariance functions associated to vector valued random fields based on latent dimensions. We also give some results for mixture based models that allow for the construction of new cross-covariance models. In particular, we give a criterion for the permissibility of quasi-arithmetic operators in order to construct valid cross covariances.

Suggested Citation

  • Porcu, Emilio & Zastavnyi, Viktor, 2011. "Characterization theorems for some classes of covariance functions associated to vector valued random fields," Journal of Multivariate Analysis, Elsevier, vol. 102(9), pages 1293-1301, October.
    • Handle: RePEc:eee:jmvana:v:102:y:2011:i:9:p:1293-1301
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    References listed on IDEAS

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    1. Tatiyana V. Apanasovich & Marc G. Genton, 2010. "Cross-covariance functions for multivariate random fields based on latent dimensions," Biometrika, Biometrika Trust, vol. 97(1), pages 15-30.
    2. Porcu, Emilio & Mateu, Jorge & Christakos, George, 2009. "Quasi-arithmetic means of covariance functions with potential applications to space-time data," Journal of Multivariate Analysis, Elsevier, vol. 100(8), pages 1830-1844, September.
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    Cited by:

    1. Jun, Mikyoung, 2014. "Matérn-based nonstationary cross-covariance models for global processes," Journal of Multivariate Analysis, Elsevier, vol. 128(C), pages 134-146.
    2. M. Ruiz-Medina & J. Angulo & G. Christakos & R. Fernández-Pascual, 2016. "New compactly supported spatiotemporal covariance functions from SPDEs," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 25(1), pages 125-141, March.
    3. Moreva, Olga & Schlather, Martin, 2023. "Bivariate covariance functions of Pólya type," Journal of Multivariate Analysis, Elsevier, vol. 194(C).
    4. Bonfim, Rafaela N. & Menegatto, Valdir A., 2016. "Strict positive definiteness of multivariate covariance functions on compact two-point homogeneous spaces," Journal of Multivariate Analysis, Elsevier, vol. 152(C), pages 237-248.
    5. 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.
    6. Kleiber, William & Nychka, Douglas, 2012. "Nonstationary modeling for multivariate spatial processes," Journal of Multivariate Analysis, Elsevier, vol. 112(C), pages 76-91.
    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.
    8. Alonso-Malaver, C.E. & Porcu, E. & Giraldo, R., 2015. "Multivariate and multiradial Schoenberg measures with their dimension walks," Journal of Multivariate Analysis, Elsevier, vol. 133(C), pages 251-265.
    9. Emilio Porcu & Philip A. White, 2022. "Random fields on the hypertorus: Covariance modeling and applications," Environmetrics, John Wiley & Sons, Ltd., vol. 33(1), February.
    10. Guella, Jean Carlo & Menegatto, Valdir Antonio & Porcu, Emilio, 2018. "Strictly positive definite multivariate covariance functions on spheres," Journal of Multivariate Analysis, Elsevier, vol. 166(C), pages 150-159.

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