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In this paper, we extend peaks-over-threshold analysis to extremes of functional data. Threshold exceedances defined using a functional r are modelled by the generalised r-Pareto process, a functional generalisation of the generalised Pareto distribution that covers the three classical regimes for the decay of tail probabilities, and that is the only possible continuous limit for r-exceedances of a properly rescaled process. We give construction rules, simulation algorithms and inference procedures for generalised r-Pareto processes, discuss model validation and apply the new methodology to extreme European windstorms and heavy spatial rainfall.<\/jats:p>","DOI":"10.1111\/rssb.12498","type":"journal-article","created":{"date-parts":[[2022,5,20]],"date-time":"2022-05-20T07:36:07Z","timestamp":1653032167000},"page":"1392-1422","source":"Crossref","is-referenced-by-count":35,"title":["Functional Peaks-Over-Threshold Analysis"],"prefix":"10.1093","volume":"84","author":[{"given":"Rapha\u00ebl","family":"de Fondeville","sequence":"first","affiliation":[{"name":"Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne (EPFL) , Lausanne , Switzerland"},{"name":"Institute of Mathematics , Lausanne , Switzerland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Anthony C.","family":"Davison","sequence":"additional","affiliation":[{"name":"Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne (EPFL) , Lausanne , Switzerland"},{"name":"Institute of Mathematics , Lausanne , Switzerland"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2022,5,20]]},"reference":[{"issue":"1","key":"2023030906301309600_","doi-asserted-by":"crossref","first-page":"99","DOI":"10.2307\/3212152","article-title":"Extreme value theory for a class of discrete distributions with applications to some stochastic processes","volume":"7","author":"Anderson","year":"1970","journal-title":"Journal of Applied Probability"},{"issue":"4","key":"2023030906301309600_","doi-asserted-by":"crossref","first-page":"2023","DOI":"10.1214\/15-AOAS863","article-title":"Extremes on river networks","volume":"9","author":"Asadi","year":"2015","journal-title":"Annals of Applied Statistics"},{"issue":"5","key":"2023030906301309600_","doi-asserted-by":"crossref","first-page":"792","DOI":"10.1214\/aop\/1176996548","article-title":"Residual life time at great age","volume":"2","author":"Balkema","year":"1974","journal-title":"The Annals of Probability"},{"key":"2023030906301309600_","doi-asserted-by":"crossref","DOI":"10.1002\/0470012382","volume-title":"Statistics of extremes: theory and applications","author":"Beirlant","year":"2004"},{"key":"2023030906301309600_","volume-title":"Ereignisanalyse Hochwasser 2005, Teil 1 \u2013 Prozessse, Sch\u00e4den und erste Einordnung","author":"Bezzola","year":"2007"},{"issue":"6","key":"2023030906301309600_","doi-asserted-by":"crossref","first-page":"763","DOI":"10.1127\/0941-2948\/2005\/0085","article-title":"Daily North-Atlantic Oscillation (NAO) index: statistics and its stratospheric polar vortex dependence","volume":"14","author":"Blessing","year":"2005","journal-title":"Meteorologische Zeitschrift"},{"issue":"2","key":"2023030906301309600_","doi-asserted-by":"crossref","first-page":"146","DOI":"10.1007\/BF01581422","article-title":"Empirical orthogonal function (eof) analysis of spatial random fields: theory, accuracy of the numerical approximations and sampling effects","volume":"7","author":"Braud","year":"1993","journal-title":"Stochastic Hydrology and Hydraulics"},{"issue":"4","key":"2023030906301309600_","doi-asserted-by":"crossref","first-page":"732","DOI":"10.2307\/3213346","article-title":"Extreme values of independent stochastic processes","volume":"14","author":"Brown","year":"1977","journal-title":"Journal of Applied Probability"},{"issue":"4","key":"2023030906301309600_","doi-asserted-by":"crossref","first-page":"1212","DOI":"10.1080\/10618600.2015.1086656","article-title":"High-order composite likelihood inference for max-stable distributions and processes","volume":"25","author":"Castruccio","year":"2016","journal-title":"Journal of Computational and Graphical Statistics"},{"issue":"3-4","key":"2023030906301309600_","doi-asserted-by":"crossref","first-page":"613","DOI":"10.1016\/j.jhydrol.2009.06.005","article-title":"Ensemble flood forecasting: a review","volume":"375","author":"Cloke","year":"2009","journal-title":"Journal of Hydrology"},{"key":"2023030906301309600_","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4471-3675-0","volume-title":"An introduction to statistical modeling of extreme values","author":"Coles","year":"2001"},{"key":"2023030906301309600_","doi-asserted-by":"crossref","first-page":"377","DOI":"10.1111\/j.2517-6161.1991.tb01830.x","article-title":"Modelling extreme multivariate events","volume":"53","author":"Coles","year":"1991","journal-title":"Journal of the Royal Statistical Society, Series B (Methodological)"},{"issue":"1","key":"2023030906301309600_","first-page":"1","article-title":"Statistical methods for multivariate extremes: an application to structural design (with discussion)","volume":"43","author":"Coles","year":"1994","journal-title":"Journal of the Royal Statistical Society. 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