Characterizations and Examples of Hidden Regular Variation

By Krishanu Maulik, Sidney I. Resnick. 2004

114 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Finance, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/5c5ea035fd2f6de9945b9de3d4053cb532f3dfc6

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Citations in the corpus

Asymptotics of random contractions (2010, methodology): “…distributional and asymptotic properties of random contractions are Kotz and Nadarajah (2000), Galambos and Simonelli (2004), Gomes et al. (2004), Maulik and Resnick (2004), Tang and Tsitsiashvili (2003, 2004), Jessen and Mikosch (2006), D’Auria and Resnick (2006, 2008), Tang (2006, 2008),…”
On a Theorem of Breiman and a Class of Random Difference Equations (2007, unknown): “A partial result in this direction has recently been obtained in [18].”
Regularly varying functions (2006, background): “(3) An example of this kind, attributed to Daren Cline, is given in Maulik and Resnick [38].”
Asymptotic Tail Probabilities of Sums of Dependent Subexponential Random Variables (2009, background): “One easily sees that, for every distribution F ∈ L, there is some function a(·) : [0,∞) → [0,∞) such that the following items hold simultaneously: a(x) → ∞, a(x) = o(x), F (x ± a(x)) ∼ F(x).”
A new class of models for bivariate joint tails (2009, background): “This is our finding more generally, and transforming to unit Fréchet via marginal empirical distributions is our favoured approach whenever only dependence features are of interest (see Ramos and Ledford (2005)).”
Living on the Multidimensional Edge: Seeking Hidden Risks Using Regular Variation (2011, methodology): “This conclusion may be naive and building on the seminal concept of coefficient of tail dependence [13], [14], hidden regular variation (HRV) [20] was introduced as a refinement of the approximation; see [7], [15], and [17].”
Determining the dependence structure of multivariate extremes (2018, background): “idden regular variation The concept of hidden regular variation was introduced by Resnick (2002), who formalized and extended the ideas of Ledford and Tawn (1996, 1997). Further work has been done by Maulik and Resnick (2004) and Mitra and Resnick (2011), for example, whilst Resnick (2007) provides ”
Regularly Varying Measures on Metric Spaces: Hidden Regular Variation and Hidden Jumps (2013, result): “This is an elaboration of results in [30, 33, 34].”
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.”
Hidden regular variation and the rank transform (2005, background): “but vo can be either finite or infinite on E0 (Maulik and Resnick (2005), Resnick (2002)) and, when we transform vo to polar coordinates, we obtain”
Detecting a conditional extreme value model (2009, background): “…literature on the behavior of multivariate extreme-value theory both in the presence of asymptotic dependence and asymptotic independence (Coles and Tawn, 1991, Ledford and Tawn, 1996, 1997, 1998, de Haan and de Ronde, 1998, Resnick, 2002, Maulik and Resnick, 2005, de Haan and Ferreira, 2006).”
Limit Laws for Random Vectors with an Extreme Component (2005, background): “α(tn) tn a, α(tn) tn b , Y∗ tn >1 =0 RANDOM VECTORS WITH AN EXTREME COMPONENT 21 giving a contradiction. So α(·) is of smaller order than tand 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 d”
Extreme behaviour for bivariate elliptical distributions (2005, background): “…value theory is generally regarded as the standard tool for modeling such events, despite the fact that several authors have recently pointed out their possible limitations; see, e.g., Bruun & Tawn (1998), Heffernan & Tawn (2004), Maulik & Resnick (2004), or Abdous, Fougères & Ghoudi (2004a).”