Detecting a conditional extreme value model

By Bikramjit Das, Sidney I. Resnick. 2009

47 citations recorded by the source corpus.

In classical extreme value theory probabilities of extreme events are estimated assuming all the components of a random vector to be in a domain of attraction of an extreme value distribution. In contrast, the conditional extreme value model assumes a domain of attraction condition on a sub-collection of the components of a multivariate random vector. This model has been studied in Heffernan and Tawn (JRSS B 66(3):497–546, 2004), Heffernan and Resnick (Ann Appl Probab 17(2):537–571, 2007), and Das and Resnick (2009). In this paper we propose three statistics which act as tools to detect this model in a bivariate set-up. In addition, the proposed statistics also help to distinguish between two forms of the limit measure that is obtained in the model.

Subfields: Finance, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/39cd7b03338971f339e762ed355a099329928a9a

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Citations in the corpus

Regularly Varying Measures on Metric Spaces: Hidden Regular Variation and Hidden Jumps (2013, background): “For example, in R+, for a risk vector X = (X1, X2), if we need to estimate P [X > x] = P [X1 > x1, X2 > x2] for large x, should the state space for asymptotic analysis be [0,∞]2 r {(0, 0)} or (0,∞]2? Ambiguity for the choice of asymptotic regime led to the idea of coefficient of tail dependence [10,”
Dimension reduction in multivariate extreme value analysis (2015, background): “On account of the nice properties of the rank transform (Das and Resnick, 2011; Heffernan and Resnick, 2005; Resnick, 2007), we can reasonably hope that these statistical objects converge to the true quantities they approximate as nÑ 8, provided at least that kÆ fulfills the usual conditions kÆ kÆn…”
Conditioning on an extreme component: Model consistency with regular variation on cones (2008, methodology): “Statistical methods for detecting when a CEV model is appropriate and whether the limit measure is a product are given in [3]: (1) Suppose that (X,Y ) satisfy Definition 1.”