Inference in multivariate Archimedean copula models

Genest, Christian; Nešlehová, Johanna; Ziegel, Johanna F.

doi:10.1007/s11749-011-0250-6

Cited by 56 publications

(61 citation statements)

References 40 publications

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“…2.1, Genest et al (2011) recall multiplicative frailty models, leading to the classical model(s) with survival copula of the Archimedean type where the generator is the Laplace transform of a distribution function F on the positive real line, i.e.,…”

Section: The Laplace-transform Approachmentioning

confidence: 99%

Comments on: Inference in multivariate Archimedean copula models

Embrechts

Hofert

2011

TEST

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Section: The Laplace-transform Approachmentioning

confidence: 99%

Comments on: Inference in multivariate Archimedean copula models

Embrechts

Hofert

2011

TEST

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“…The elements of this class may be characterized by a continuous, strictly decreasing and convex function Φ : [0, The function Φ is called the generator of C and its pseudo-ineverse Φ [−1] (t) is defined as the usual inverse Φ −1 (t) for t ∈ [0, Φ(0)] and is set to 0 for t ≥ Φ (0). The prominence of the class of Archimedean copulas basically stems from the fact that they are easy to handle and to simulate, see Genest et al (2011). While the estimation of Archimedean copulas has been investigated in Genest and Rivest (1993) and recently more thoroughly in Genest et al (2011), the issue of testing for the hypothesis that the copula is an Archimedean one has found much less interest in the literature.…”

Section: Introductionmentioning

confidence: 99%

“…The prominence of the class of Archimedean copulas basically stems from the fact that they are easy to handle and to simulate, see Genest et al (2011). While the estimation of Archimedean copulas has been investigated in Genest and Rivest (1993) and recently more thoroughly in Genest et al (2011), the issue of testing for the hypothesis that the copula is an Archimedean one has found much less interest in the literature. The present paper fills this gap by developing a consistent test for this hypothesis.…”

Section: Introductionmentioning

confidence: 99%

A test for Archimedeanity in bivariate copula models

Bücher

Dette

Volgushev

2012

Journal of Multivariate Analysis

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We propose a new test for the hypothesis that a bivariate copula is an Archimedean copula. The test statistic is based on a combination of two measures resulting from the characterization of Archimedean copulas by the property of associativity and by a strict upper bound on the diagonal by the Fréchet-upper bound. We prove weak convergence of this statistic and show that the critical values of the corresponding test can be determined by the multiplier bootstrap method. The test is shown to be consistent against all departures from Archimedeanity if the copula satisfies weak smoothness assumptions. A simulation study is presented which illustrates the finite sample properties of the new test.

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“…. , n and estimate the γ parameter (e.g., Embrechts and Hofert 2013;Genest et al 2011, and references therein), and we then estimate the σ i parameters based on the univariate marginal distributions assuming that the γ parameter is known. Given the cumbersome form of p.d.f.…”

Section: Theoretical Considerationsmentioning

confidence: 99%

On a Multiplicative Multivariate Gamma Distribution with Applications in Insurance

Semenikhine

Furman

2018

Risks

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Abstract:One way to formulate a multivariate probability distribution with dependent univariate margins distributed gamma is by using the closure under convolutions property. This direction yields an additive background risk model, and it has been very well-studied. An alternative way to accomplish the same task is via an application of the Bernstein-Widder theorem with respect to a shifted inverse Beta probability density function. This way, which leads to an arguably equally popular multiplicative background risk model (MBRM), has been by far less investigated. In this paper, we reintroduce the multiplicative multivariate gamma (MMG) distribution in the most general form, and we explore its various properties thoroughly. Specifically, we study the links to the MBRM, employ the machinery of divided differences to derive the distribution of the aggregate risk random variable explicitly, look into the corresponding copula function and the measures of nonlinear correlation associated with it, and, last but not least, determine the measures of maximal tail dependence. Our main message is that the MMG distribution is (1) very intuitive and easy to communicate, (2) remarkably tractable, and (3) possesses rich dependence and tail dependence characteristics. Hence, the MMG distribution should be given serious considerations when modelling dependent risks.

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Inference in multivariate Archimedean copula models

Abstract: Archimedean copula, Consistency, Frailty, Kendall distribution, Probability integral transform, Radial distribution, Simplex distribution, Weak convergence, 62G05, 62G20, 62H12, 62H20,

Cited by 56 publications

References 40 publications

Comments on: Inference in multivariate Archimedean copula models

Comments on: Inference in multivariate Archimedean copula models

A test for Archimedeanity in bivariate copula models

On a Multiplicative Multivariate Gamma Distribution with Applications in Insurance

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