A few generalizations of Kendall’s tau. Part I: Construction
Complimenting our earlier work on generalizations of popular concordance measures in the sense of Scarsini for a pair of continuous random variables (X, Y) (such measures can be understood as functions of the bivariate copula C associated with (X, Y)), we focus on generalizations of Kendall’s τ. In...
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| Language: | English |
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Vilnius University Press
2024-06-01
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| Series: | Nonlinear Analysis |
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| Online Access: | https://www.journals.vu.lt/nonlinear-analysis/article/view/35460 |
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| author | Martynas Manstavičius |
| author_facet | Martynas Manstavičius |
| author_sort | Martynas Manstavičius |
| collection | DOAJ |
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Complimenting our earlier work on generalizations of popular concordance measures in the sense of Scarsini for a pair of continuous random variables (X, Y) (such measures can be understood as functions of the bivariate copula C associated with (X, Y)), we focus on generalizations of Kendall’s τ. In Part I, we give two forms of such measures and also provide general bounds for their values, which are sharp in certain cases and depend on the values of Spearman’s ρ and the original Kendall’s τ. Part II is devoted to the intrinsic meaning of presented Kendall’s τ generalizations, their degree as polynomial-type concordance measures, and computational aspects.
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| format | Article |
| id | doaj-art-e8e66bb3135d4a03b5e6f82c7e20eeb2 |
| institution | OA Journals |
| issn | 1392-5113 2335-8963 |
| language | English |
| publishDate | 2024-06-01 |
| publisher | Vilnius University Press |
| record_format | Article |
| series | Nonlinear Analysis |
| spelling | doaj-art-e8e66bb3135d4a03b5e6f82c7e20eeb22025-08-20T02:03:58ZengVilnius University PressNonlinear Analysis1392-51132335-89632024-06-0129410.15388/namc.2024.29.35460A few generalizations of Kendall’s tau. Part I: ConstructionMartynas Manstavičius0https://orcid.org/0000-0002-2802-0025Vilnius University Complimenting our earlier work on generalizations of popular concordance measures in the sense of Scarsini for a pair of continuous random variables (X, Y) (such measures can be understood as functions of the bivariate copula C associated with (X, Y)), we focus on generalizations of Kendall’s τ. In Part I, we give two forms of such measures and also provide general bounds for their values, which are sharp in certain cases and depend on the values of Spearman’s ρ and the original Kendall’s τ. Part II is devoted to the intrinsic meaning of presented Kendall’s τ generalizations, their degree as polynomial-type concordance measures, and computational aspects. https://www.journals.vu.lt/nonlinear-analysis/article/view/35460Kendall’s tauScarsini axiomsbivariate copulatransformationconcordance measuresupermodular |
| spellingShingle | Martynas Manstavičius A few generalizations of Kendall’s tau. Part I: Construction Nonlinear Analysis Kendall’s tau Scarsini axioms bivariate copula transformation concordance measure supermodular |
| title | A few generalizations of Kendall’s tau. Part I: Construction |
| title_full | A few generalizations of Kendall’s tau. Part I: Construction |
| title_fullStr | A few generalizations of Kendall’s tau. Part I: Construction |
| title_full_unstemmed | A few generalizations of Kendall’s tau. Part I: Construction |
| title_short | A few generalizations of Kendall’s tau. Part I: Construction |
| title_sort | few generalizations of kendall s tau part i construction |
| topic | Kendall’s tau Scarsini axioms bivariate copula transformation concordance measure supermodular |
| url | https://www.journals.vu.lt/nonlinear-analysis/article/view/35460 |
| work_keys_str_mv | AT martynasmanstavicius afewgeneralizationsofkendallstauparticonstruction AT martynasmanstavicius fewgeneralizationsofkendallstauparticonstruction |