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Aggregation-cokriging for highly multivariate spatial data

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  • Reinhard Furrer
  • Marc G. Genton

Abstract

Best linear unbiased prediction of spatially correlated multivariate random processes, often called cokriging in geostatistics, requires the solution of a large linear system based on the covariance and cross-covariance matrix of the observations. For many problems of practical interest, it is impossible to solve the linear system with direct methods. We propose an efficient linear unbiased predictor based on a linear aggregation of the covariables. The primary variable together with this single meta-covariable is used to perform cokriging. We discuss the optimality of the approach under different covariance structures, and use it to create reanalysis type high-resolution historical temperature fields. Copyright 2011, Oxford University Press.

Suggested Citation

  • Reinhard Furrer & Marc G. Genton, 2011. "Aggregation-cokriging for highly multivariate spatial data," Biometrika, Biometrika Trust, vol. 98(3), pages 615-631.
    • Handle: RePEc:oup:biomet:v:98:y:2011:i:3:p:615-631
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    File URL: http://hdl.handle.net/10.1093/biomet/asr029
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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. Jorge G. Adrover & Stella M. Donato, 2023. "Aspects of robust canonical correlation analysis, principal components and association," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 32(2), pages 623-650, June.
    3. Krupskii, Pavel & Genton, Marc G., 2019. "A copula model for non-Gaussian multivariate spatial data," Journal of Multivariate Analysis, Elsevier, vol. 169(C), pages 264-277.
    4. Bachoc, François & Genton, Mark G. & Nordhausen, Klaus & Ruiz-Gazen, Anne & Virta, Joni, 2019. "Spatial Blind Source Separation," TSE Working Papers 19-998, Toulouse School of Economics (TSE).
    5. Adrover, Jorge G. & Donato, Stella M., 2015. "A robust predictive approach for canonical correlation analysis," Journal of Multivariate Analysis, Elsevier, vol. 133(C), pages 356-376.
    6. Seokhyun Chung & Raed Al Kontar & Zhenke Wu, 2022. "Weakly Supervised Multi-output Regression via Correlated Gaussian Processes," INFORMS Joural on Data Science, INFORMS, vol. 1(2), pages 115-137, October.

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