Extremal attractors of Liouville copulas

Belzile, Léo R.; Nešlehová, Johanna

doi:10.1016/j.jmva.2017.05.008

Cited by 13 publications

(15 citation statements)

References 38 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The family of stable tail dependence functions with spectral density (6.10) is a special case of the scaled extremal Dirichlet model derived in [2]. As shown therein, this model has a simple stochastic representation which is stated and proved below in the specific case of h G ρ .…”

Section: Gumbel and Galambos Brought Togethermentioning

confidence: 95%

See 1 more Smart Citation

When Gumbel met Galambos

Genest

Nešlehová

2017

Copulas and Dependence Models With Applications

Self Cite

View full text Add to dashboard Cite

show abstract

Section: Gumbel and Galambos Brought Togethermentioning

confidence: 95%

“…Beyond highlighting the kinship between the Gumbel and Galambos families of copulas, formulas (6.12)-(6.13) lead to a unified simulation algorithm for these two dependence structures. This procedure, adapted from [7,35], is presented in a broader context in [2]. Gumbel and Galambos are thereby united, at last.…”

Section: Gumbel and Galambos Brought Togethermentioning

confidence: 99%

When Gumbel met Galambos

Genest

Nešlehová

2017

Copulas and Dependence Models With Applications

Self Cite

View full text Add to dashboard Cite

show abstract

“…This is because it holds whenever 1/R with R as in (2.3) is in the domain of attraction of the Fréchet (Φ α ), Gumbel (Λ) or Weibull (Ψ α ) distributions for some α > 0, in notation 1/R ∈ M(Φ α ), 1/R ∈ M(Λ) or 1/R ∈ M(Ψ α ). Moreover, Condition 4.1 with m = 1 further holds as soon as E(1/R 1+ ) < ∞ for some > 0, see Proposition 2 in [4].…”

Section: Conditionsmentioning

confidence: 99%

Inference for Archimax copulas

Chatelain¹,

Fougères²,

Nešlehová³

2020

Ann. Statist.

Self Cite

View full text Add to dashboard Cite

Archimax copula models can account for any type of asymptotic dependence between extremes and at the same time capture joint risks at medium levels. An Archimax copula C ψ, is characterized by two functional parameters, the stable tail dependence function , and the Archimedean generator ψ which acts as a distortion of the extreme-value dependence model. This article develops semiparametric inference for Archimax copulas: a nonparametric estimator of and a moment-based estimator of ψ assuming the latter belongs to a parametric family. Conditions under which ψ and are identifiable are derived. The asymptotic behavior of the estimators is then established under broad regularity conditions; performance in small samples is assessed through a comprehensive simulation study. The Archimax copula model with the Clayton generator is then used to analyze monthly rainfall maxima at three stations in French Brittany. The model is seen to fit the data very well, both in the lower and in the upper tail. The nonparametric estimator of reveals asymmetric extremal dependence between the stations, which reflects heavy precipitation patterns in the area. Technical proofs, simulation results and R code are provided in the Appendix.

show abstract

“…The exponent function given in their Theorem 1 matches equation (6). In their Theorem 2, Belzile and Nešlehová (2018) consider the extremal dependence properties of 1/(X 1 , X 2 ) =R(W 1 ,W 2 ), i.e., the Liouville copula itself. Since the reciprocal of Dirichlet random variables have regularly varying tails, this links with Proposition 5 which states that asymptotic independence arises if (W 1 ,W 2 ) themselves are asymptotically independent and heavier-tailed than R. Proposition 6(3c) is relevant ifR andW are regularly varying with the same index.…”

Section: Literature Review and Examplesmentioning

confidence: 99%

Extremal dependence of random scale constructions

2019

View full text Add to dashboard Cite

A bivariate random vector can exhibit either asymptotic independence or dependence between the largest values of its components. When used as a statistical model for risk assessment in fields such as finance, insurance or meteorology, it is crucial to understand which of the two asymptotic regimes occurs. Motivated by their ubiquity and flexibility, we consider the extremal dependence properties of vectors with a random scale construction (X1, X2) = R(W1, W2), with non-degenerate R > 0 independent of (W1, W2). Focusing on the presence and strength of asymptotic tail dependence, as expressed through commonly-used summary parameters, broad factors that affect the results are: the heaviness of the tails of R and (W1, W2), the shape of the support of (W1, W2), and dependence between (W1, W2). When R is distinctly lighter tailed than (W1, W2), the extremal dependence of (X1, X2) is typically the same as that of (W1, W2), whereas similar or heavier tails for R compared to (W1, W2) typically result in increased extremal dependence. Similar tail heavinesses represent the most interesting and technical cases, and we find both asymptotic independence and dependence of (X1, X2) possible in such cases when (W1, W2) exhibit asymptotic independence. The bivariate case often directly extends to higher-dimensional vectors and spatial processes, where the dependence is mainly analyzed in terms of summaries of bivariate sub-vectors. The results unify and extend many existing examples, and we use them to propose new models that encompass both dependence classes.

show abstract

Extremal attractors of Liouville copulas

Cited by 13 publications

References 38 publications

When Gumbel met Galambos

When Gumbel met Galambos

Inference for Archimax copulas

Extremal dependence of random scale constructions

Contact Info

Product

Resources

About