Modeling Nonstationary Extreme Dependence With Stationary Max-Stable Processes and Multidimensional Scaling

Chevalier, Clément; Martius, Olivia; Ginsbourger, David (2021). Modeling Nonstationary Extreme Dependence With Stationary Max-Stable Processes and Multidimensional Scaling. Journal of computational and graphical statistics : JCGS, 30(3), pp. 745-755. American Statistical Association 10.1080/10618600.2020.1844213

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Modeling the joint distribution of extreme events at multiple locations is a challenging task with important applications. In this study, we use max-stable models to study extreme daily precipitation events in Switzerland. The non-stationarity of the spatial process at hand involves important challenges, which are often dealt with by using a stationary model in a so-called climate space, with well-chosen covariates. Here, we instead choose to warp the weather stations under study in a latent space of higher dimension using multidimensional scaling (MDS). Two methods are proposed to define target dissimilarity matrices, based respectively on extremal coefficients and on pairwise likelihoods. Results suggest that the proposed methods allow capturing complex spatial dependences of spatial extreme precipitations, enabling in turn to reliably extrapolate functionals such as extremal coefficients.

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