On all Pickands Dependence Functions whose corresponding Extreme-Value-Copulas have Spearman ρ (Kendall τ) identical to some value v ∈ [0,1]

2018/01/23 by Noppadon Kamnitui, Kamnitui, Noppadon, Christian Genest +3
Mathematics · #FOS: Mathematics #Mathematical Approximation and Integration #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.1801.07665

openalex publication_date 2018/01/23 · openalex created_date 2022/09/03 · openalex updated_date 2026/07/28

Abstract

We answer an open question posed by the second author at the Salzburg workshop on Dependence Models and Copulas in 2016 concerning the size of the family A^ρ_v (A^τ_v) of all Pickands dependence functions A whose corresponding Extreme-Value-Copulas have Spearman ρ (Kendall τ) equal to some arbitrary, fixed value v ∈ [0,1]. After determining compact sets Ω^ρ_v, Ω^τ_v ⊆ [0,1] × [(1)/(2),1] containing the graphs of all Pickands dependence functions from the classes A^ρ_v and A^τ_v respectively, we then show that both sets are best possible.

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