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Extra-parametrized extreme value copula : Extension to a spatial framework
Spatial Statistics ( IF 2.3 ) Pub Date : 2020-01-24 , DOI: 10.1016/j.spasta.2020.100410
J. Carreau , G. Toulemonde

Hazard assessment at a regional scale may be performed thanks to a spatial model for maxima that can be obtained by combining the generalized extreme-value (GEV) distribution for the univariate marginal distributions with extreme-value copulas to describe their dependence structure, as justified by the theory of multivariate extreme values. A flexible class of extreme-value copulas, called XGumbel for short, combines two Gumbel copulas with extra-parameters weighting each dimension. In a multisite study, the XGumbel copula quickly becomes over-parametrized. In addition, interpolation to ungauged locations is not easily achieved. We develop an extension of the XGumbel copula to the spatial framework by defining the extra-parameters as a mapping shaped as a disk. The inference of the Spatialized XGumbel copula is performed thanks to an Approximate Bayesian Computation (ABC) scheme with summary statistics based on upper tail dependence coefficients. The GEV parameters are estimated with a spatial regression model built with a vector generalized linear model. We evaluate and compare this spatial model with the Brown–Resnick process on annual maxima of daily precipitation totals at 177 gauged stations in the French Mediterranean over a 57 year period. Our analyses show that the ABC scheme yields, except in one instance, interpretable parameters. In addition, the Spatialized XGumbel copula is able to reproduce reasonably well the non-stationarity present in our case study.



中文翻译:

超参数化极值copula:扩展到空间框架

得益于最大空间模型,可以通过将单变量边际分布的广义极值(GEV)分布与极值copulas相结合来描述其依赖结构来获得区域规模的危害评估,如多元极值理论。灵活的一类极值copula,简称XGumbel,将两个Gumbel copula组合在一起,每个参数都对每个维度加权。在多站点研究中,XGumbel copula很快变得过参数化。另外,不容易实现对未测量位置的插值。通过将额外参数定义为磁盘形状的映射,我们将XGumbel copula扩展到空间框架。由于采用了基于上尾部依赖系数的汇总统计的近似贝叶斯计算(ABC)方案,因此可以进行空间化XGumbel copula的推断。GEV参数通过使用向量广义线性模型构建的空间回归模型进行估算。我们对这种空间模型进行了评估,并将其与布朗-雷斯尼克过程进行了比较,比较了57年间法国地中海地区177个测量站日降水总量的年度最大值。我们的分析表明,除一种情况外,ABC方案产生可解释的参数。此外,Spatialized XGumbel copula能够很好地再现本案例研究中存在的非平稳性。GEV参数通过使用向量广义线性模型构建的空间回归模型进行估算。我们对这种空间模型进行了评估,并将其与布朗-雷斯尼克过程进行了比较,比较了57年间法国地中海地区177个测量站日降水总量的年度最大值。我们的分析表明,除一种情况外,ABC方案产生可解释的参数。此外,Spatialized XGumbel copula能够合理地重现我们的案例研究中存在的非平稳性。GEV参数通过使用向量广义线性模型构建的空间回归模型进行估算。我们对这种空间模型进行了评估,并将其与布朗-雷斯尼克过程进行了比较,比较了57年间法国地中海地区177个测量站日降水总量的年度最大值。我们的分析表明,除一种情况外,ABC方案产生可解释的参数。此外,Spatialized XGumbel copula能够很好地再现本案例研究中存在的非平稳性。在一种情况下,除了可解释的参数。此外,Spatialized XGumbel copula能够很好地再现本案例研究中存在的非平稳性。在一种情况下,除了可解释的参数。此外,Spatialized XGumbel copula能够很好地再现本案例研究中存在的非平稳性。

更新日期:2020-01-24
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