Hidden Regular Variation, Second Order Regular Variation and Asymptotic Independence

By Sidney I. Resnick. 2002

196 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Finance, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/1fc6dcfd6ddace3adb82cebd6231d7b2c147c022

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Citations in the corpus

Dimension reduction in multivariate extreme value analysis (2015, background): “This inconclusive example suggests that extending our approach to the analysis of the hidden angular measure (Resnick, 2002, 2008) would be of major interest.”
Conditioning on an extreme component: Model consistency with regular variation on cones (2008, background): “Heffernan and Tawn (2004) and Heffernan and Resnick (2007) developed an approximation to the joint distribution of the random vector by conditioning that one of the components be extreme.”
Detecting a conditional extreme value model (2009, background): “Multivariate extreme value theory assumes an extreme-valued domain of attraction condition on the joint distribution of a random vector which after a suitable standardization relates multivariate extreme value theory to regular variation on Rd+. Probabilities of critical risk events can be…”
Hidden regular variation and the rank transform (2005, background): “Sidney Resnick’s research was partially supported by NSF grant DMS-0303493 and grant MSPF-02G-183 from the Mathematical Sciences Program of the NSA.”
A new representation for multivariate tail probabilities (2013, background): “non-degenerate, and c(n) = o(n), n → ∞. In representation (1.3), the sequence c(n), is a regularly varying function of n with index η, whilst the limit measure ν is homogeneous of order −1/η (Resnick [20, 22]). Multivariate tail probabilities 3 Ledford and Tawn [14] phrased their original condition ”
Heavy tailed time series with extremal independence (2013, background): “tremely large. The suitably renormalized componentwise maxima of an i.i.d. sequence of extremally independent random vectors converge to a max-stable distribution with independent marginals. See e.g. [Res02] or [Res07]. This deﬁnition is rather weak and it must be noted that if two components of the”
Modeling Spatial Processes with Unknown Extremal Dependence Class (2017, unknown): “where LW : (0,∞) → (0,∞) is slowly varying at infinity, that is, LW (ax)/LW (x) → 1 as x → ∞ for any a > 0, and 0 < ηW (h) < 1 for h = s j − sk = 0 (Ledford and Tawn 1996; Resnick 2002).”
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”
Quotient correlation: A sample based alternative to Pearson’s correlation (2008, background): “…delay, and design a better network structure, there have been a series of studies on tail dependence between internet traffic variables, for instance by Campos et al. (2003), Maulik, Resnick and Rootzén (2002), Resnick (2001, 2002), Zhang, Breslau, Paxson and Shenker (2002) and many others.”
Determining the dependence structure of multivariate extremes (2018, background): “, Resnick (2010)), lim t→∞ pr(R > tr,W ∈ B | R > t) = H(B)r−1, (2)”
Tail asymptotics for the sum of two heavy-tailed dependent risks (2006, background): “see Resnick (2004). Finally, the tail dependence coefficient λ as defined in Section 1 can in this case be obtained by considering the event jXj=x > t for t 1⁄4 1 minf cosφ; sinφg in Eq.”
Modelling across extremal dependence classes (2014, methodology): “Since ‖ · ‖a is arbitrary, we henceforth use the L1-norm, ‖ · ‖1, and redefine H to be the limiting distribution of W = XP /(XP + YP ), with H(w) = H([0, w]) (0 ≤ w ≤ 1).”
Living on the Multidimensional Edge: Seeking Hidden Risks Using Regular Variation (2011, methodology): “If the limit measure μ(·) in (1) concentrates on the axes, the traditional definition of HRV [Resnick, 2002] removes the axes and defines hidden regular variation on the cone (0,∞]2.”