Bivariate Distributions with Given Extreme Value Attractor

By P. Capéraà, Anne-Laure Fougères, Christian Genest. 2000

170 citations recorded by the source corpus.

Subfields: Demography, Finance, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/f3f91255dbbf8a464c185afe9ea2ee1680dd8386

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Citations in the corpus

Use of a Gaussian copula for multivariate extreme value analysis: Some case studies in hydrology (2007, background): “Although specific copulas have been proposed to account for the theoretical properties of extremes [4, 22], additional developments are still needed, especially in the field of spatial extremes.”
A new class of models for bivariate joint tails (2009, background): “All bivariate extreme value (BEV) dependence structures and the great majority of dependence structures that exist within the copula literature have extremal dependence structures that can be represented in the form (1.2); see Capéraà et al. (2000) and Heffernan (2000).”
Multivariate hydrological frequency analysis using copulas (2004, methodology): “We are considering the use of copulas with two or more parameters, for example the Archimax copulas [Capéraà et al., 2000], which encompass the Archimedean copulas and extreme value distributions as special cases.”
Bivariate drought frequency analysis using the copula method (2012, background): “However, only a few of them have found practical applications (Joe 1997; Nelsen 2006; Capéraà et al. 2000; Fang et al. 2002; Abdous et al. 2004).”
Extreme-value copulas (2009, background): “If the following limit exists, then the domain-of-attraction condition (6) is veriﬁed for C F equal to C f , the tail dependence function being for ( x 1 ,... , x d ) ∈ [ 0 , ¥ ) d ; see [8, 11].”
Detecting Dependence With Kendall Plots (2003, methodology): “…implication C = C ¤ ) K = K ¤ is false may be veri ed easily using the class of bivariate extreme-value distributions,whose underlyingcopulas (see, e.g.,Caṕera³a, Foug³eres, and Genest 1997b, 2000) are of the form CA(u; v) = exp · log(uv)A ½ log(u) log(uv) ¾¸ for some convex functionA : [0; 1] !”
Estimating the tail-dependence coefficient: Properties and pitfalls (2005, background): “Remarks. i) Archimedean copulas that belong to a domain of attraction are necessarily in the domain of attraction of the Gumbel copula, which is an EV copula; see, e.g., Genest and Rivest (1989) and Capéraà et al. (2000).”
Conditions for the Asymptotic Semiparametric Efficiency of an Omnibus Estimator of Dependence Parame (2000, methodology): “…this remains to be checked in full generality, the nature of condition (5) makes it improbable that the omnibus estimator θ̂ is semiparametrically efficient for any of the most common parametric copula models, say within the broad Archimax class recently introduced by Capéraà et al. (2000).”
Goodness‐of‐fit Procedures for Copula Models Based on the Probability Integral Transformation (2006, unknown): “For additional details see, for instance, Tawn (1988), Capéraà et al. (1997, 2000) or Capéraà & Fougères (2001).”
Everything You Always Wanted to Know about Copula Modeling but Were Afraid to Ask (2007, unknown): “See, for example, Ghoudi et al. 1998 or Caperaa et al. 2000 .”