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    Cross-covariance functions for multivariate random fields based on latent dimensions

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    Type
    Article
    Authors
    Apanasovich, T. V.
    Genton, M. G.
    Date
    2010-02-16
    Online Publication Date
    2010-02-16
    Print Publication Date
    2010-03-01
    Permanent link to this record
    http://hdl.handle.net/10754/597897
    
    Metadata
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    Abstract
    The problem of constructing valid parametric cross-covariance functions is challenging. We propose a simple methodology, based on latent dimensions and existing covariance models for univariate random fields, to develop flexible, interpretable and computationally feasible classes of cross-covariance functions in closed form. We focus on spatio-temporal cross-covariance functions that can be nonseparable, asymmetric and can have different covariance structures, for instance different smoothness parameters, in each component. We discuss estimation of these models and perform a small simulation study to demonstrate our approach. We illustrate our methodology on a trivariate spatio-temporal pollution dataset from California and demonstrate that our cross-covariance performs better than other competing models. © 2010 Biometrika Trust.
    Citation
    Apanasovich TV, Genton MG (2010) Cross-covariance functions for multivariate random fields based on latent dimensions. Biometrika 97: 15–30. Available: http://dx.doi.org/10.1093/biomet/asp078.
    Sponsors
    The authors are grateful to the editor, an associate editor and two anonymous referees for theirvaluable comments. This research was sponsored by the National Science Foundation, U.S.A.,and by an award made by the King Abdullah University of Science and Technology
    Publisher
    Oxford University Press (OUP)
    Journal
    Biometrika
    DOI
    10.1093/biomet/asp078
    ae974a485f413a2113503eed53cd6c53
    10.1093/biomet/asp078
    Scopus Count
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