Modelling across extremal dependence classes

By Jennifer L. Wadsworth, Jonathan A. Tawn, A. C. Davison, D. Elton. 2014

83 citations recorded by the source corpus.

Different dependence scenarios can arise in multivariate extremes, entailing careful selection of an appropriate class of models. In bivariate extremes, the variables are either asymptotically dependent or are asymptotically independent. Most available statistical models suit one or other of these cases, but not both, resulting in a stage in the inference that is unaccounted for but can substantially impact subsequent extrapolation. Existing modelling solutions to this problem are either applicable only on subdomains or appeal to multiple limit theories. We introduce a unified representation for bivariate extremes that encompasses a wide variety of dependence scenarios and applies when at least one variable is large. Our representation motivates a parametric model that encompasses both dependence classes. We implement a simple version of this model and show that it performs well in a range of settings.

Subfields: Economics and Econometrics, Finance

View Paper: https://www.semanticscholar.org/paper/1827443410e3350ccb494806c21e2914b990e12d

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Citations in the corpus

Modeling Spatial Processes with Unknown Extremal Dependence Class (2017, methodology): “Notice that margins are here available in closed form, unlike the Gaussian scale mixture model of Huser, Opitz, and Thibaud (2017), or the bivariate model of Wadsworth et al. (2017). Since the copula is the object of interest in all of the above cases, this makes model (4) computationally more appea”
Bridging asymptotic independence and dependence in spatial extremes using Gaussian scale mixtures (2016, methodology): “In contrast, the pseudo-polar representations of multivariate limit distributions have motivated Wadsworth et al. (2017) to explore how more ﬂexible transitions between dependence classes can be achieved in the bivariate case through a common random scaling applied to a random vector on the unit…”
Graphical models for extremes (2018, background): “…satisfies the pairwise Markov property Yi ⊥e Yj|Y\{i,j}, .i, j/ ∈E: .1/ The main advantage of conditional independence and graphical models is that they imply a simple probabilistic structure and possibly sparse patterns in multivariate random vectors (Lauritzen, 1996; Wainwright and Jordan, 2008).”