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    Gaussian likelihood inference on data from trans-Gaussian random fields with Matérn covariance function

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    2017.YG.Environmetrics.final.pdf
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    Type
    Article
    Authors
    Yan, Yuan cc
    Genton, Marc G. cc
    KAUST Department
    Applied Mathematics and Computational Science Program
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Statistics Program
    Date
    2017-07-12
    Online Publication Date
    2017-07-12
    Print Publication Date
    2018-08
    Permanent link to this record
    http://hdl.handle.net/10754/625682
    
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    Abstract
    Gaussian likelihood inference has been studied and used extensively in both statistical theory and applications due to its simplicity. However, in practice, the assumption of Gaussianity is rarely met in the analysis of spatial data. In this paper, we study the effect of non-Gaussianity on Gaussian likelihood inference for the parameters of the Matérn covariance model. By using Monte Carlo simulations, we generate spatial data from a Tukey g-and-h random field, a flexible trans-Gaussian random field, with the Matérn covariance function, where g controls skewness and h controls tail heaviness. We use maximum likelihood based on the multivariate Gaussian distribution to estimate the parameters of the Matérn covariance function. We illustrate the effects of non-Gaussianity of the data on the estimated covariance function by means of functional boxplots. Thanks to our tailored simulation design, a comparison of the maximum likelihood estimator under both the increasing and fixed domain asymptotics for spatial data is performed. We find that the maximum likelihood estimator based on Gaussian likelihood is overall satisfying and preferable than the non-distribution-based weighted least squares estimator for data from the Tukey g-and-h random field. We also present the result for Gaussian kriging based on Matérn covariance estimates with data from the Tukey g-and-h random field and observe an overall satisfactory performance.
    Citation
    Yan Y, Genton MG (2017) Gaussian likelihood inference on data from trans-Gaussian random fields with Matérn covariance function. Environmetrics: e2458. Available: http://dx.doi.org/10.1002/env.2458.
    Sponsors
    This research was supported by the King Abdullah University of Science and Technology (KAUST).
    Publisher
    Wiley
    Journal
    Environmetrics
    DOI
    10.1002/env.2458
    Additional Links
    http://onlinelibrary.wiley.com/doi/10.1002/env.2458/abstract
    ae974a485f413a2113503eed53cd6c53
    10.1002/env.2458
    Scopus Count
    Collections
    Articles; Applied Mathematics and Computational Science Program; Statistics Program; Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division

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