Detecting a conditional extreme value model

Das, Bikramjit; Resnick, Sidney I.

doi:10.1007/s10687-009-0097-3

Cited by 33 publications

(35 citation statements)

References 25 publications

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“…Due to the importance of conditional limit theorems and conditional extreme value models (see Heffernan and Resnick 2007;Das and Resnick 2010) we provide a conditional limit result for χ 2 -distributions. We focus for simplicity on the 2-dimensional setup considering ξ n = (ξ n1 , ξ n2 ) , n ≥ 1, as in Eq.…”

Section: Discussionmentioning

confidence: 99%

Extremes of independent chi-square random vectors

Hashorva

Kabluchko²,

Wübker

2010

Extremes

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Section: Discussionmentioning

confidence: 99%

Extremes of independent chi-square random vectors

Hashorva

Kabluchko²,

Wübker

2010

Extremes

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“…Section 3.6 gives techniques for detecting when data is consistent with a model exhibiting MRV and HRV. These techniques rely on the fact that under broad conditions, if a vector X has a multivariate regularly varying distribution on a cone C, then under a generalized polar coordinate transformation (see (2.6)), the transformed vector satisfies a conditional extreme value (CEV) model for which detection techniques exist from [10]. This methodology adds to the toolbox of one dimensional techniques such as checking if one dimensional marginal distributions are heavy tailed or checking whether one dimensional functions of the data vector such as the maximum and the minimum component are heavy tailed.…”

Section: Das and Resnickmentioning

confidence: 99%

Hidden regular variation under full and strong asymptotic dependence

Das

Resnick

2017

Extremes

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Data exhibiting heavy-tails in one or more dimensions is often studied using the framework of regular variation. In a multivariate setting this requires identifying specific forms of dependence in the data; this means identifying that the data tends to concentrate along particular directions and does not cover the full space. This is observed in various data sets from finance, insurance, network traffic, social networks, etc. In this paper we discuss the notions of full and strong asymptotic dependence for bivariate data along with the idea of hidden regular variation in these cases. In a risk analysis setting, this leads to improved risk estimation accuracy when regular methods provide a zero estimate of risk. Analyses of both real and simulated data sets illustrate concepts of generation and detection of such models.28A33, 60G70, 62G05, 62G32.

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“…These techniques rely on the fact that under broad conditions, if a vector X has a multivariate regularly varying distribution on a cone C, then under a generalized polar coordinate transformation (see (1.4) (CEV) model for which detection techniques exist from [8]. Our methodology is more reliable than one dimensional techniques such as checking if one dimensional marginal distributions are heavy tailed or checking whether one dimensional functions of the data vector such as the maximum and the minimum component are heavy tailed.…”

Section: 2mentioning

confidence: 99%

Models with Hidden Regular Variation: Generation and Detection

Das

Resnick

2015

Stochastic Systems

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We review the notions of multivariate regular variation (MRV) and hidden regular variation (HRV) for distributions of random vectors and then discuss methods for generating models exhibiting both properties concentrating on the non-negative orthant in dimension two. Furthermore we suggest diagnostic techniques that detect these properties in multivariate data and indicate when models exhibiting both MRV and HRV are plausible fits for the data. We illustrate our techniques on simulated data, as well as two real Internet data sets.1. Introduction. This paper discusses methods for constructing multivariate heavy-tailed models on particular sub-cones of R 2 + = [0, ∞) 2 by adapting techniques from multivariate regular variation theory. We evaluate two different methods for generating models exhibiting multiple heavy-tailed regimes. The results obtained in the different regimes are governed by the sub-cone that serves as the state-space, the choice of scaling function, and often the interaction between different regimes. We also discuss statistical detection methods which validate that data is consistent with particular multivariate heavy-tailed models; these methods are adapted from those developed for the conditional extreme value model (CEV) [8]. We discuss multivariate regular variation (MRV) on the cones R 2 + \ {0} and (0, ∞) 2 . When regular variation exists on both cones, the regular variation on the smaller cone (0, ∞) 2 is called hidden regular variation (HRV).Data that may be modeled by distributions having heavy tails appear in many contexts, for example, hydrology [1], finance [31], insurance [14], Internet traffic [6], social networks and random graphs [3,13,28,30] and risk

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Detecting a conditional extreme value model

Cited by 33 publications

References 25 publications

Extremes of independent chi-square random vectors

Extremes of independent chi-square random vectors

Hidden regular variation under full and strong asymptotic dependence

Models with Hidden Regular Variation: Generation and Detection

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