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Séminaires DSA

Bridging Asymptotic Independence and Dependence in Spatial Extremes Using Gaussian Scale Mixtures

Thomas Opitz (Biostatistics and Spatial Processes, INRA, Avignon, France)

28 février 2017  -  11:00-12:00, salle Extranef 109

The classical max-stable limit models for spatial extremes are well suited for asymptotically dependent data whose  strength of spatial dependence between extreme observations at different locations remains stable when moving towards more extreme levels. In contrast, the empirical exploration of the spatial extremal dependence in climatic data often suggests that convergence to the limiting dependence has not yet taken place, and the assumption of asymptotic dependence is at the least contestable. On this ground, it is preferable to propose flexible subasymptotic extremal dependence models that smoothly bridge asymptotic independence and dependence. In this context, we consider  the dependence structure induced by Gaussian scale mixture processes for modeling high threshold exceedances. After studying the extremal dependence properties of Gaussian scale mixtures, we propose a flexible yet parsimonious parametric copula model that smoothly interpolates from asymptotic dependence to independence and includes the Gaussian dependence as a special case. We show how this new model can be fitted to high threshold exceedances using a censored likelihood approach. In particular, this parametric approach borrows strength across locations for better estimation of the asymptotic dependence class. We demonstrate the capacity of our methodology by adequately capturing the extremal properties of wind speed data collected in the Pacific Northwest, US.

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