000261330 001__ 261330 000261330 005__ 20190509131804.0 000261330 0247_ $$2doi$$a10.5075/epfl-thesis-8927 000261330 037__ $$aTHESIS 000261330 041__ $$aeng 000261330 088__ $$a8927 000261330 245__ $$aFunctional Peaks-Over-Threshold Analysis for Complex Extreme Events 000261330 260__ $$c2018$$bEPFL$$aLausanne 000261330 269__ $$a2018 000261330 300__ $$a201 000261330 336__ $$aTheses 000261330 502__ $$aProf. Victor Panaretos (président) ; Prof. Anthony C. Davison (directeur de thèse) ; Prof. Stephan Morgenthaler, Prof. Holger Rootzén, Prof. Clément Dombry (rapporteurs) 000261330 520__ $$aMost current risk assessment for complex extreme events relies on catalogues of similar events, either historical or generated artificially. In the latter, no existing methods produce completely new events with mathematically justified extrapolation above observed level of severity. This thesis contributes to the development of stochastic generators of events based on extreme value theory, with a special focus on natural hazards. The sources of historical meteorological records are multiple but climate model output is attractive for its spatial completeness and homogeneity. From a statistical perspective, these are massive gridded data sets, which can be exploited for accurate estimation of extreme events. The first contribution of this thesis describes methods of statistical inference for extremal processes that are computationally tractable for large data sets. We also relate the extremal behaviour of aggregated data to point observations, a result that we use to downscale gridded data to local tail distributions. These contributions are illustrated by applications to rainfall and heatwaves. Building stochastic generators of extreme events requires the extension of classical peaks-over-threshold analysis to continuous stochastic processes. We develop a framework in which characterization of complex extremes can be motivated by field-specific expertise. The contribution includes the description of the theoretical limiting distribution of functional exceedances, called the generalized r-Pareto process, the functional equivalent of the generalized Pareto distribution, for which we describe statistical inference procedures, simulation algorithms and goodness-of-fit diagnostics. We apply these results to build a stochastic weather generator of extreme wind storms over Europe. 000261330 592__ $$b2018 000261330 6531_ $$aCensored likelihood 000261330 6531_ $$aDownscaling 000261330 6531_ $$aExtreme value theory 000261330 6531_ $$aGeneralized r-Pareto process 000261330 6531_ $$aGradient score 000261330 6531_ $$aHigh-dimensional inference 000261330 6531_ $$aNatural hazards 000261330 6531_ $$aSpatio-temporal statistics 000261330 6531_ $$aStochastic processes 000261330 6531_ $$aWind storm 000261330 700__ $$0248398$$ade Deloÿe et Fourcade de Fondeville, Raphaël Gérard Théodore Michel Marie$$g244252 000261330 720_2 $$aDavison, Anthony C.$$edir.$$g111184 000261330 8564_ $$uhttps://infoscience.epfl.ch/record/261330/files/EPFL_TH8927.pdf$$s33369335 000261330 909C0 $$pSTAT 000261330 909CO $$pthesis$$pthesis-public$$pDOI$$pSB$$ooai:infoscience.epfl.ch:261330$$qGLOBAL_SET 000261330 918__ $$dEDMA$$cMATHAA$$aSB 000261330 919__ $$aSTAT 000261330 920__ $$a2018-12-07$$b2018 000261330 970__ $$a8927/THESES 000261330 973__ $$sPUBLISHED$$aEPFL 000261330 980__ $$aTHESIS