The generalized Pareto process; with a view towards application and simulation

By Ana Ferreira, Laurens de Haan. 2012

151 citations recorded by the source corpus.

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 $\mathbb {R}^d$. 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.

Subfields: Finance, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/31aa18e88ba45818e6421b40206007eb60ad0395

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Citations in the corpus

Functional regular variations, Pareto processes and peaks over threshold (2015, background): “For a background on functional extreme value theory, we refer to the monograph de Haan and Ferreira [8].”
Space–time modelling of extreme events (2012, methodology): “Genton et al. (2011) provide a closed-form expression of the likelihood function for the Smith max-stable model indexed by R when N ≤ d + 1, and Huser and Davison (2013) have generalized this to the Brown–Resnick process, but only the bivariate margins are known for other models.”
Bridging asymptotic independence and dependence in spatial extremes using Gaussian scale mixtures (2016, background): “For Model 1, we transpose the arguments of Wadsworth et al. (2017) concerning the choice of the random scaling in pseudo-polar representations to our framework, and we model the random scale through a generalized Pareto distribution, The distribution (17 Model 2 provides high ﬂexibility in both the ”
Multivariate peaks over thresholds models (2016, unknown): “This is the Ferreira and de Haan (2014) spectral representation transformed to the exponential scale. and GP S ( σ , γ , F S ) classes defined by Eqs.”
Extremes on river networks (2015, background): “(2009a,b, 2013) describe an alternative approach to modelling joint flooding that allows the possibility of asymptotically independent extremes through the fitting of the Heffernan and Tawn (2004) model.”
A Horse Race between the Block Maxima Method and the Peak–over–Threshold Approach (2018, methodology): “Recent development on Generalized Pareto Processes allow for considering parametric estimation for the dependence structure, see, e.g. Ferreira and De Haan (2014), Thibaud and Opitz (2015) and Huser and Wadsworth (2017).”