MAX-STABLE MODELS FOR MULTIVARIATE EXTREMES

By Johan Segers. 2012

81 citations recorded by the source corpus.

Multivariate extreme-value analysis is concerned with the extremes in a multivariate random sample, that is, points of which at least some components have exceptionally large values. Mathematical theory suggests the use of max-stablemodels for univariate and multivariate extremes. A comprehensive account is given of the various ways in which max-stable models are described. Furthermore, a construction device is proposed for generating parametric families of max-stable distributions. Although the device is not new, its role as a model generator seems not yet to have been fully exploited.

Subfields: Finance, Global and Planetary Change, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/1016376c22b2fee9b9c8fcf0282be8eaa56fed51

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Citations in the corpus

Factor Copula Models for Replicated Spatial Data (2015, methodology): “Extreme-value copulas are tailored for extremes and can capture tail dependence © American Statistical Association and asymmetry (Segers 2012), but computation of joint densities is excessively prohibitive in high dimensions (Castruccio, Huser, and Genton 2016), which makes them difficult to use.”
Likelihood estimators for multivariate extremes (2014, methodology): “…extremes consists in approximating the distribution of componentwise finite-block maxima by flexible parametric asymptotic submodels, proposed among others by Gumbel (1961), Tawn (1988), Hüsler and Reiss (1989), Coles and Tawn (1991), Joe et al. (1992), Demarta and McNeil (2005) and Segers (2012).”
Modeling the spatial dependence of floods using the Fisher copula (2019, methodology): “…with their main catchment characteristics and an abbreviation that will be used in the sequel of this paper to refer to the individual stations For each of the measurement stations, an hourly runoff time series spanning 30 to 40 years was available from the Federal Ofﬁce for the Environment”
Modeling Spatial Processes with Unknown Extremal Dependence Class (2017, background): “…{1 − (tx1)−1} , . . . , Xd ≤ F−1X { 1 − (txd )−1 }]) , which describes the joint dependence of the associated maxstable or generalized Pareto process, see Davison, Padoan, and Ribatet (2012), Cooley et al. (2012), Segers (2012), or Davison and Huser (2015) for recent reviews on max-stable models.”
Determining the dependence structure of multivariate extremes (2018, background): “C.3 A max-mixture distribution Segers (2012) shows how to construct distributions that place extremal mass on different combinations of faces of the angular unit simplex.”