Hidden regular variation and the rank transform

By Janet E. Heffernan, Sidney I. Resnick. Advances in Applied Probability, 2005

50 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/48a36b0273c1a92cb979fa840f9b4c4492c60b4f

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Citations in the corpus

Conditioning on an extreme component: Model consistency with regular variation on cones (2008, background): “Keywords: asymptotic independence; conditional extreme value model; domain of attraction; regular variation”
Limit Laws for Random Vectors with an Extreme Component (2005, methodology): “So α(·) is of smaller order than t and we have the situation of hidden regular variation [20, 27, 36]; that is, the regular variation condition (37) holds on the big cone [0,∞]2 \ {0} but a different regular variation condition holds on the smaller cone [0,∞] × (0,∞].”
Geostatistics of extremes (2012, background): “More recent work on these lines is by Heffernan & Resnick (2005, 2007).”
Copulas: Tales and facts (2006, background): “An extreme value copula is derived from a multivariate EVD by transforming its marginals to the unit cube [0, 1]n. Multivariate EVDs occur as weak limits of affinely transformed vectors of component-wise maxima of iid random variables; see Resnick [24], Chapter 5.”
A new representation for multivariate tail probabilities (2013, background): “Specifically, the assumption in Heffernan and Resnick [9] can be expressed in exponential margins as there exist functions s(n)> 0, r(n) such that P({XE − r(n)}/s(n)≤ x|YE > logn)→H(x) as n→∞ for some non-degenerate distribution function H .”
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…”
Living on the Multidimensional Edge: Seeking Hidden Risks Using Regular Variation (2011, methodology): “In [7], [15], and [20] HRV on (0,∞]2 was considered and in [17] the cone E = {x ∈ [0,∞]d : x(l) > 0} was considered.”
A new class of models for bivariate joint tails (2009, background): “See Resnick (2002), Maulik and Resnick (2004) and Heffernan and Resnick (2005) for precise treatments.”
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,”