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Name: Raphael de Fondeville 

Talk Title: Sub-asymptotic Models for Functional Peaks-over-threshold Modelling

Abstract: Functional peaks-over-threshold analysis has recently been introduced as the generalization to functions of the classical, and widely applied, univariate methodology. In this framework, functional exceedances are defined through a real valued functional, called risk functional, allowing to characterize and study complex extreme events. In practice, functional peaks-over-threshold analysis is attractive for its versatility in terms of risk definition, and the existence of models for which inference procedures are tractable in high-dimensions. These models, due to their asymptotic nature, are however likely to lack flexibility when applied to limited quantity of data. Indeed, when analysing events of increasing levels of intensity, decreasing trends in dependence have been observed in multiple environmental applications. To accommodate for such phenomenon, we propose several sub-asymptotic models based on log-Gaussian random functions that can be estimated using existing inference techniques and we give their regime of asymptotic dependence. This work offers to analysts realistic models that can be estimated in high-dimension with the freedom to choose between regimes of extremal dependence depending on their aversion to risk. We illustrate the models attractiveness and flexibility on several case studies.

This talk is an invited talk at EVA 2021. View the programme here.