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- W4289543322 abstract "In the present paper, we study extreme negative dependence focussing on the concordance order for copulas. With the absence of a least element for dimensions $dge$ 3, the set of all minimal elements in the collection of all copulas turns out to be a natural and quite important extreme negative dependence concept. We investigate several sufficient conditions and we provide a necessary condition for a copula to be minimal: The sufficient conditions are related to the extreme negative dependence concept of d-countermonotonicity and the necessary condition is related to the collection of all copulas minimizing multivariate Kendall's tau. The concept of minimal copulas has already been proved to be useful in various continuous and concordance order preserving optimization problems including variance minimization and the detection of lower bounds for certain measures of concordance. We substantiate this key role of minimal copulas by showing that every continuous and concordance order preserving functional on copulas is minimized by some minimal copula and, in the case the continuous functional is even strictly concordance order preserving, it is minimized by minimal copulas only. Applying the above results, we may conclude that every minimizer of Spearman's rho is also a minimizer of Kendall's tau." @default.
- W4289543322 created "2022-08-03" @default.
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- W4289543322 date "2018-09-17" @default.
- W4289543322 modified "2023-09-24" @default.
- W4289543322 title "On Minimal Copulas under the Concordance Order" @default.
- W4289543322 doi "https://doi.org/10.48550/arxiv.1809.06099" @default.
- W4289543322 hasPublicationYear "2018" @default.
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