Carreau Julie, Toulemonde G. (2020). Extra-parametrized extreme value copula : extension to a spatial framework. Spatial Statistics, 40 (no spécial), 100410 [20 p.]. ISSN 2211-6753.
Titre du document
Extra-parametrized extreme value copula : extension to a spatial framework
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.
Plan de classement
Sciences fondamentales / Techniques d'analyse et de recherche [020]
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Hydrologie [062]
