On the extremal dependence coefficient of multivariate distributions

Frahm, Gabriel

doi:10.1016/j.spl.2006.03.006

Cited by 49 publications

(38 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…First, they are exchangeable, a fact that could represented a limitation in some applications. Second, their tail behavior is only driven by the generator function F. To make this statement precise, consider the following extremal dependence coefficient introduced in [13]. …”

Section: Theorem 3 Let F : [0 1] → [0 1] Be a Continuous Df Andmentioning

confidence: 99%

Copulas Based on Marshall–Olkin Machinery

Durante

Girard

Mazo

2015

Springer Proceedings in Mathematics &Amp; Statistics

View full text Add to dashboard Cite

We present a general construction principle for copulas that is inspired by the celebrated Marshall-Olkin exponential model. From this general construction method we derive special sub-classes of copulas that could be useful in different situations and recall their main properties. Moreover, we discuss possible estimation strategy for the proposed copulas. The presented results are expected to be useful in the construction of stochastic models for lifetimes (e.g. in reliability theory) or in credit risk models.

show abstract

Section: Theorem 3 Let F : [0 1] → [0 1] Be a Continuous Df Andmentioning

confidence: 99%

Copulas Based on Marshall–Olkin Machinery

Durante

Girard

Mazo

2015

Springer Proceedings in Mathematics &Amp; Statistics

View full text Add to dashboard Cite

show abstract

“…Furthermore, simulation from an asymmetric multivariate stable distributions turns out to be difficult hindering the use of indirect inference estimation methods, as precisely these methods are appropriate when simulating from the model of interest is straightforward. 15 An alternative is to use a recent method proposed by Nolan (2005), which is based on projections parameter functions. Another alternative is the use of generalized elliptical distributions (cf.…”

Section: Resultsmentioning

confidence: 99%

“…For instance, the symmetric generalized hyperbolic distribution is also appropriate. The choice of the Student's t motivated by Demarta and McNeil (2005), Frahm, Junker and Szimayer (2005) and Frahm (2006) whom suggest that this distribution as a reference model for elliptically contoured distributions. 8 In actual facts, it is not strictly necessary to work with standard maximum likelihood, and more efficient algorithms such as the EM (Meng and van Dijk, 1995) can be employed.…”

Section: Elliptical Distributionsmentioning

confidence: 99%

Indirect estimation of elliptical stable distributions

Lombardi

Veredas

2009

Computational Statistics & Data Analysis

View full text Add to dashboard Cite

We present an indirect estimation approach for elliptical stable distributions which relies on the use of a multivariate t distribution as auxiliary model. This distribution is also elliptical and we show that its parameters have a one-to-one relationship with those of the elliptical stable, therefore making the proposed indirect approach especially suitable. Standard asymptotic properties are also shown and we analyze the finite sample behavior of the estimators via a comprehensive Monte Carlo study. An application to 27 emerging markets stock indexes concludes the paper.

show abstract

“…In mathematical finance, U .X sWd jX d kC1Wd / can be viewed as the limiting conditional probability that X sWd violates its value-at-risk at level 1 t , given that X d kC1Wd has done so. If s D k D 1, we obtain the upper extremal dependence coefficient, U , considered in [7]. The study of systemic stability is also an important issue within the context of extreme risk dependence.…”

Section: Measures Of Tail Dependencementioning

confidence: 99%