Abstract:The classical tail dependence coefficient (TDC) may fail to capture non-exchangeable features of bivariate tail dependence since it evaluates the underlying copula only along the diagonal. To address this limitation, several measures of strongest manifestation of tail dependence have been proposed in the bivariate case, including a measure based on the tail copula of the underlying bivariate copula. This paper introduces and investigates the multivariate maximal tail concordance measure (MTCM) which extends the bivariate measure to the multivariate case. The MTCM quantifies the largest tail mass over lower hyperrectangles of common unit volume, while the associated maximizer identifies the direction of maximal tail probability. We establish fundamental properties of the MTCM in the multivariate case, including existence of an optimal direction. We also derive analytical representations for several important model classes. Closed-form expressions are further obtained for survival Marshall-Olkin copulas, Archimax and nested Archimedean copulas with regularly varying Archimedean generators. An application to trivariate annual sea-level maxima in England shows that the MTCM can reveal off-diagonal stress directions and substantial differences in the underlying extremal dependence not detected by likelihood- or TDC-based comparisons.
| Subjects: | Statistics Theory (math.ST); Risk Management (q-fin.RM) |
| Cite as: | arXiv:2605.25766 [math.ST] |
| (or arXiv:2605.25766v1 [math.ST] for this version) | |
| https://doi.org/10.48550/arXiv.2605.25766 arXiv-issued DOI via DataCite (pending registration) |
From: Takaaki Koike [view email]
[v1]
Mon, 25 May 2026 12:19:02 UTC (121 KB)
此内容由惯性聚合(RSS阅读器)自动聚合整理，仅供阅读参考。 原文来自 — 版权归原作者所有。