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    Bridging asymptotic independence and dependence in spatial exbtremes using Gaussian scale mixtures

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    Type
    Article
    Authors
    Huser, Raphaël cc
    Opitz, Thomas
    Thibaud, Emeric
    KAUST Department
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Statistics Program
    Date
    2017-06-23
    Online Publication Date
    2017-06-23
    Print Publication Date
    2017-08
    Permanent link to this record
    http://hdl.handle.net/10754/625177
    
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    Abstract
    Gaussian scale mixtures are constructed as Gaussian processes with a random variance. They have non-Gaussian marginals and can exhibit asymptotic dependence unlike Gaussian processes, which are asymptotically independent except in the case of perfect dependence. In this paper, we study the extremal dependence properties of Gaussian scale mixtures and we unify and extend general results on their joint tail decay rates in both asymptotic dependence and independence cases. Motivated by the analysis of spatial extremes, we propose flexible yet parsimonious parametric copula models that smoothly interpolate from asymptotic dependence to independence and include the Gaussian dependence as a special case. We show how these new models can be fitted to high threshold exceedances using a censored likelihood approach, and we demonstrate that they provide valuable information about tail characteristics. In particular, by borrowing strength across locations, our parametric model-based approach can also be used to provide evidence for or against either asymptotic dependence class, hence complementing information given at an exploratory stage by the widely used nonparametric or parametric estimates of the χ and χ̄ coefficients. We demonstrate the capacity of our methodology by adequately capturing the extremal properties of wind speed data collected in the Pacific Northwest, US.
    Citation
    Huser R, Opitz T, Thibaud E (2017) Bridging asymptotic independence and dependence in spatial exbtremes using Gaussian scale mixtures. Spatial Statistics. Available: http://dx.doi.org/10.1016/j.spasta.2017.06.004.
    Sponsors
    We thank Amanda Hering (Baylor University) for sharing the wind data and Luigi Lombardo (KAUST) for cartographic support. This work was undertaken while Emeric Thibaud was at Colorado State University with partial support by US National Science Foundation Grant DMS-1243102. Thomas Opitz was partially supported by the French national programme LEFE/INSU .
    Publisher
    Elsevier BV
    Journal
    Spatial Statistics
    DOI
    10.1016/j.spasta.2017.06.004
    arXiv
    1610.04536
    Additional Links
    http://www.sciencedirect.com/science/article/pii/S221167531730088X
    ae974a485f413a2113503eed53cd6c53
    10.1016/j.spasta.2017.06.004
    Scopus Count
    Collections
    Articles; Statistics Program; Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division

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