2012/03/31 by Ana Ferreira, Laurens de Haan · 1 citation
Mathematics · #math.PR
paper · pdf · doi:10.3150/13-bej538
published as Bernoulli 2014, Vol. 20, No. 4, 1717-1737 · Published in at http://dx.doi.org/10.3150/13-BEJ538 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)
arxiv created 2014/10/16 · arxiv updated 2014/10/17
In extreme value statistics, the peaks-over-threshold method is widely used. The method is based on the generalized Pareto distribution characterizing probabilities of exceedances over high thresholds in \mathbb Rd. We present a generalization of this concept in the space of continuous functions. We call this the generalized Pareto process. Differently from earlier papers, our definition is not based on a distribution function but on functional properties, and does not need a reference to a related max-stable process. As an application, we use the theory to simulate wind fields connected to disastrous storms on the basis of observed extreme but not disastrous storms. We also establish the peaks-over-threshold approach in function space.