{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,11]],"date-time":"2026-06-11T11:08:48Z","timestamp":1781176128194,"version":"3.54.1"},"reference-count":29,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2026,2,20]],"date-time":"2026-02-20T00:00:00Z","timestamp":1771545600000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Journal of Computational and Applied Mathematics"],"published-print":{"date-parts":[[2026,10]]},"DOI":"10.1016\/j.cam.2026.117466","type":"journal-article","created":{"date-parts":[[2026,2,21]],"date-time":"2026-02-21T16:12:35Z","timestamp":1771690355000},"page":"117466","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":2,"special_numbering":"C","title":["On the exact region between Chatterjee\u2019s rank correlation and Spearman\u2019s footrule"],"prefix":"10.1016","volume":"485","author":[{"ORCID":"https:\/\/orcid.org\/0009-0005-1818-3831","authenticated-orcid":false,"given":"Marcus","family":"Rockel","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"78","reference":[{"key":"10.1016\/j.cam.2026.117466_bib0001","first-page":"229","article-title":"Fonctions de r\u00e9partition \u00e0 n dimensions et leur marges","volume":"8","author":"Sklar","year":"1960","journal-title":"Publ. Inst. Stat. Univ."},{"issue":"536","key":"10.1016\/j.cam.2026.117466_bib0002","doi-asserted-by":"crossref","DOI":"10.1080\/01621459.2020.1758115","article-title":"A new coefficient of correlation","volume":"116","author":"Chatterjee","year":"2009","journal-title":"J. Amer. Statist. Assoc."},{"issue":"1","key":"10.1016\/j.cam.2026.117466_bib0003","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1111\/j.1467-9469.2011.00767.x","article-title":"A copula-based non-parametric measure of regression dependence","volume":"40","author":"Dette","year":"2013","journal-title":"Scand. J. Stat."},{"key":"10.1016\/j.cam.2026.117466_bib0004","series-title":"An Introduction to Copulas. 2nd ed","author":"Nelsen","year":"2006"},{"issue":"8","key":"10.1016\/j.cam.2026.117466_bib0005","doi-asserted-by":"crossref","first-page":"937","DOI":"10.1080\/10485250903499667","article-title":"Spearman\u2019s footrule and Gini\u2019s gamma: a review with complements","volume":"22","author":"Genest","year":"2010","journal-title":"J. Nonparametr. Stat."},{"issue":"4","key":"10.1016\/j.cam.2026.117466_bib0006","first-page":"600","article-title":"Copulas and Markov processes","volume":"36","author":"Darsow","year":"1992","journal-title":"Ill. J. Math."},{"key":"10.1016\/j.cam.2026.117466_bib0007","series-title":"Technical Report","article-title":"The exact region determined by Spearman\u2019s footrule, Gini\u2019s gamma and Kendall\u2019s tau","author":"Damjana","year":"2026"},{"issue":"13","key":"10.1016\/j.cam.2026.117466_bib0008","article-title":"On the exact region determined by Spearman\u2019s footrule and Gini\u2019s gamma","volume":"410","author":"Kokol","year":"2022","journal-title":"J. Comput. Appl. Math."},{"issue":"3","key":"10.1016\/j.cam.2026.117466_bib0009","first-page":"16","article-title":"On the exact regions determined by Kendall\u2019s tau and other concordance measures","volume":"20","author":"Kokol","year":"2023","journal-title":"Mediterr. J. Math."},{"key":"10.1016\/j.cam.2026.117466_bib0010","first-page":"23","article-title":"On the exact region determined by Spearman\u2019s rho and Spearman\u2019s footrule","volume":"437","author":"Kokol","year":"2024","journal-title":"J. Comput. Appl. Math."},{"key":"10.1016\/j.cam.2026.117466_bib0011","article-title":"Spearman\u2019s footrule and Gini\u2019s gamma: local bounds for bivariate copulas and the exact region with respect to Blomqvist\u2019s beta","volume":"390","author":"Bukov\u0161ek","year":"2021","journal-title":"J. Comput. Appl. Math."},{"key":"10.1016\/j.cam.2026.117466_bib0012","doi-asserted-by":"crossref","DOI":"10.1016\/j.cam.2024.116259","article-title":"Revisiting the region determined by Spearman\u2019s \u03c1 and Spearman\u2019s footrule \u03d5","volume":"457","author":"Tschimpke","year":"2025","journal-title":"J. Comput. Appl. Math."},{"key":"10.1016\/j.cam.2026.117466_bib0013","series-title":"Technical Report","article-title":"The exact region and an inequality between chatterjee\u2019s and spearman\u2019s rank correlations","author":"Ansari","year":"2025"},{"key":"10.1016\/j.cam.2026.117466_bib0014","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1016\/j.jmva.2023.105266","article-title":"Quantifying directed dependence via dimension reduction","volume":"201","author":"Fuchs","year":"2024","journal-title":"J. Multivariate Anal."},{"issue":"2","key":"10.1016\/j.cam.2026.117466_bib0015","first-page":"14","article-title":"Stochastic monotonicity and the Markov product for copulas","volume":"503","author":"Friedrich","year":"2021","journal-title":"J. Math. Anal. Appl."},{"key":"10.1016\/j.cam.2026.117466_bib0016","series-title":"Probability and measure","author":"Billingsley","year":"1995"},{"key":"10.1016\/j.cam.2026.117466_bib0017","first-page":"36","article-title":"Dependence properties of bivariate copula families","volume":"12","author":"Ansari","year":"2024","journal-title":"Depend. Model."},{"key":"10.1016\/j.cam.2026.117466_bib0018","series-title":"Technical Report","article-title":"On continuity of chatterjee\u2019s rank correlation and related dependence measures","author":"Ansari","year":"2025"},{"key":"10.1016\/j.cam.2026.117466_bib0019","series-title":"Technical Report","article-title":"On exact regions between measures of concordance and chatterjee\u2019s rank correlation for lower semilinear copulas","author":"Fuchs","year":"2025"},{"key":"10.1016\/j.cam.2026.117466_bib0020","series-title":"Technical Report","article-title":"Measures of association for approximating copulas","author":"Rockel","year":"2025"},{"key":"10.1016\/j.cam.2026.117466_bib0021","series-title":"Principles of Copula Theory","author":"Fabrizio","year":"2016"},{"key":"10.1016\/j.cam.2026.117466_bib0022","series-title":"Convex functions, partial orderings, and statistical applications","volume":"187","author":"Josip","year":"1992"},{"issue":"2","key":"10.1016\/j.cam.2026.117466_bib0023","doi-asserted-by":"crossref","first-page":"690","DOI":"10.1016\/j.jmaa.2011.06.013","article-title":"On a strong metric on the space of copulas and its induced dependence measure","volume":"384","author":"Trutschnig","year":"2011","journal-title":"J. Math. Anal. Appl."},{"issue":"10","key":"10.1016\/j.cam.2026.117466_bib0024","doi-asserted-by":"crossref","first-page":"1761","DOI":"10.1016\/j.spl.2012.06.008","article-title":"On the approximation of copulas via shuffles of Min","volume":"82","author":"Fabrizio","year":"2012","journal-title":"Statist. Probab. Lett."},{"key":"10.1016\/j.cam.2026.117466_bib0025","series-title":"Algebra 2. Linear algebra, Galois theory, representation theory, group extensions and Schur multiplier","author":"Lal","year":"2017"},{"key":"10.1016\/j.cam.2026.117466_bib0026","doi-asserted-by":"crossref","first-page":"126","DOI":"10.1515\/demo-2019-0005","article-title":"On the lower bound of Spearman\u2019s footrule","volume":"7","author":"Fuchs","year":"2019","journal-title":"Depend. Model."},{"key":"10.1016\/j.cam.2026.117466_bib0027","series-title":"Technical Report","article-title":"A simple extension of Azadkia and Chatterjee\u2019s rank correlation to a vector of endogenous variables","author":"Ansari","year":"2022"},{"key":"10.1016\/j.cam.2026.117466_bib0028","series-title":"Perturbation Analysis of Optimization Problems","author":"J","year":"2000"},{"key":"10.1016\/j.cam.2026.117466_bib0029","series-title":"Metric spaces","author":"Shirali","year":"2006"}],"container-title":["Journal of Computational and Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0377042726001317?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0377042726001317?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,5,29]],"date-time":"2026-05-29T00:34:32Z","timestamp":1780014872000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0377042726001317"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,10]]},"references-count":29,"alternative-id":["S0377042726001317"],"URL":"https:\/\/doi.org\/10.1016\/j.cam.2026.117466","relation":{},"ISSN":["0377-0427"],"issn-type":[{"value":"0377-0427","type":"print"}],"subject":[],"published":{"date-parts":[[2026,10]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"On the exact region between Chatterjee\u2019s rank correlation and Spearman\u2019s footrule","name":"articletitle","label":"Article Title"},{"value":"Journal of Computational and Applied Mathematics","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.cam.2026.117466","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2026 The Author(s). Published by Elsevier B.V.","name":"copyright","label":"Copyright"}],"article-number":"117466"}}