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Nonstationary modeling for multivariate spatial processes

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  • Kleiber, William
  • Nychka, Douglas

Abstract

We derive a class of matrix valued covariance functions where the direct and cross-covariance functions are Matérn. The parameters of the Matérn class are allowed to vary with location, yielding local variances, local ranges, local geometric anisotropies and local smoothnesses. We discuss inclusion of a nonconstant cross-correlation coefficient and a valid approximation. Estimation utilizes kernel smoothed empirical covariance matrices and a locally weighted minimum Frobenius distance that yields local parameter estimates at any location. We derive the asymptotic mean squared error of our kernel smoother and discuss the case when multiple field realizations are available. Finally, the model is illustrated on two datasets, one a synthetic bivariate one-dimensional spatial process, and the second a set of temperature and precipitation model output from a regional climate model.

Suggested Citation

  • Kleiber, William & Nychka, Douglas, 2012. "Nonstationary modeling for multivariate spatial processes," Journal of Multivariate Analysis, Elsevier, vol. 112(C), pages 76-91.
    • Handle: RePEc:eee:jmvana:v:112:y:2012:i:c:p:76-91
    DOI: 10.1016/j.jmva.2012.05.011
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    13. Jun, Mikyoung & Knutti, Reto & Nychka, Douglas W, 2008. "Spatial Analysis to Quantify Numerical Model Bias and Dependence," Journal of the American Statistical Association, American Statistical Association, vol. 103(483), pages 934-947.
    14. 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.
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    Cited by:

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    3. Chunsheng Ma, 2013. "Mittag-Leffler vector random fields with Mittag-Leffler direct and cross covariance functions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 65(5), pages 941-958, October.
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    6. Rachid Senoussi & Emilio Porcu, 2022. "Nonstationary space–time covariance functions induced by dynamical systems," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(1), pages 211-235, March.
    7. Takahiro Yoshida & Morito Tsutsumi, 2018. "On the effects of spatial relationships in spatial compositional multivariate models," Letters in Spatial and Resource Sciences, Springer, vol. 11(1), pages 57-70, March.
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    10. Philip A. White & Durban G. Keeler & Daniel Sheanshang & Summer Rupper, 2022. "Improving piecewise linear snow density models through hierarchical spatial and orthogonal functional smoothing," Environmetrics, John Wiley & Sons, Ltd., vol. 33(5), August.

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