Orthant tail dependence of multivariate extreme value distributions

Li, Haijun

doi:10.1016/j.jmva.2008.04.007

Cited by 84 publications

(68 citation statements)

References 24 publications

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“…where C denotes the survival function of C. Bivariate tail dependence has been widely studied [13], and various multivariate versions of tail dependence parameters have also been introduced and studied in [16,18].…”

Section: Bounds For Tail Risks Via Tail Dependence Functionsmentioning

confidence: 99%

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Tail Risk of Multivariate Regular Variation

Joe

2010

Methodol Comput Appl Probab

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Tail risk refers to the risk associated with extreme values and is often affected by extremal dependence among multivariate extremes. Multivariate tail risk, as measured by a coherent risk measure of tail conditional expectation, is analyzed for multivariate regularly varying distributions. Asymptotic expressions for tail risk are established in terms of the intensity measure that characterizes multivariate regular variation. Tractable bounds for tail risk are derived in terms of the tail dependence function that describes extremal dependence. Various examples involving Archimedean copulas are presented to illustrate the results and quality of the bounds.

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Section: Bounds For Tail Risks Via Tail Dependence Functionsmentioning

confidence: 99%

“…of [18] that µ((1, ∞]) > 0 (see also (3.6)). Since ||X|| max is regularly varying at ∞, we have for sufficiently small 1 − p, there exists r 1,p , such that…”

Section: Bounds For Tail Risks Via Tail Dependence Functionsmentioning

confidence: 99%

Tail Risk of Multivariate Regular Variation

Joe

2010

Methodol Comput Appl Probab

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“…In the multivariate literature, the focus 50 is most often on the modeling of extremes, especially on describing the dependence of extreme 51 observations, and also providing asymptotic results (e.g. Li [2009]). However, before developing 52 these important issues (modeling and asymptotic behavior), it is important to correctly identify 53 the notion of extreme in the multivariate context.…”

Section: And the References Therein) 47mentioning

confidence: 99%

Multivariate extreme value identification using depth functions

Chebana¹,

Ouarda²

2011

Environmetrics

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“…In particular some bivariate tail dependence coefficients have been introduced by Sibuya (1960). Multivariate dependence coefficients are discussed in De Luca and Rivieccio (2012) and Li (2009). Statistical literature is also available for tail coefficients, see e.g.…”

Section: Introductionmentioning

confidence: 99%

On tail dependence coefficients of transformed multivariate Archimedean copulas

Bernardino¹,

Rullière²

2016

Fuzzy Sets and Systems

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This paper presents the impact of a class of transformations of copulas in their upper and lower multivariate tail dependence coefficients. In particular we focus on multivariate Archimedean copulas. In the first part of this paper, we calculate multivariate tail dependence coefficients when the generator of the considered copula exhibits some regular variation properties, and we investigate the behaviour of these coefficients in cases that are close to tail independence. This first part exploits previous works of Charpentier and Segers (2009) and extends some results of Juri and Wüthrich (2003) and De Luca and Rivieccio (2012). In the second part of the paper we analyse the impact in the upper and lower multivariate tail dependence coefficients of a large class of transformations of dependence structures. These results are based on the transformations exploited by Di Bernardino and Rullière (2013a) and Di Bernardino and Rullière (2013b). We extend some bivariate results of Durante et al. (2010) in a multivariate setting by calculating multivariate tail dependence coefficients for transformed copulas. We obtain new results under specific conditions involving regularly varying hazard rates of components of the transformation. In the third part, we show the utility of using transformed Archimedean copulas, as they permit to build Archimedean generators exhibiting any chosen couple of lower and upper tail dependence coefficients. Furthermore, using results in Larsson and Nešlehová (2011), we detail the extreme behaviour of the transformed radial part of Archimedean copulas. At last, we explain possible applications with Markov chains with specific dependence structure.

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Orthant tail dependence of multivariate extreme value distributions

Cited by 84 publications

References 24 publications

Tail Risk of Multivariate Regular Variation

Tail Risk of Multivariate Regular Variation

Multivariate extreme value identification using depth functions

On tail dependence coefficients of transformed multivariate Archimedean copulas

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