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#### Article: Tail-weighted dependence measures with limit being the tail dependence coefficient

Title Tail-weighted dependence measures with limit being the tail dependence coefficient Lee, DJoe, HKrupskii, P 2018 Taylor & Francis. The Journal's web site is located at http://www.tandf.co.uk/journals/titles/10485252.asp Journal of Nonparametric Statistics, 2018, v. 30, p. 262-290 How to Cite? For bivariate continuous data, measures of monotonic dependence are based on the rank transformations of the two variables. For bivariate extreme value copulas, there is a family of estimators ${\hat\vartheta}_\alpha$, for $\alpha>0$, of the extremal coefficient, based on a transform of the absolute difference of the $\alpha$ power of the ranks. In the case of general bivariate copulas, we obtain the probability limit $\zeta_\alpha$ of $\hat{\zeta}_\alpha=2-{\hat\vartheta}_\alpha$ as the sample size goes to infinity, and show that (i) $\zeta_\alpha$ for $\alpha=1$ is a measure of central dependence with properties similar to Kendall's tau and Spearman's rank correlation, (ii) $\zeta_\alpha$ is a tail-weighted dependence measure for large $\alpha$, and (iii) the limit as $\alpha\to\infty$ is the upper tail dependence coefficient. We obtain asymptotic properties for the rank-based measure ${\hat\zeta}_\alpha$, and estimate tail dependence coefficients through extrapolation on ${\hat\zeta}_\alpha$. A data example illustrates the use of the new dependence measures for tail inference. http://hdl.handle.net/10722/259500

DC FieldValueLanguage
dc.contributor.authorLee, D-
dc.contributor.authorJoe, H-
dc.contributor.authorKrupskii, P-
dc.date.accessioned2018-09-03T04:08:50Z-
dc.date.available2018-09-03T04:08:50Z-
dc.date.issued2018-
dc.identifier.citationJournal of Nonparametric Statistics, 2018, v. 30, p. 262-290-
dc.identifier.urihttp://hdl.handle.net/10722/259500-
dc.description.abstractFor bivariate continuous data, measures of monotonic dependence are based on the rank transformations of the two variables. For bivariate extreme value copulas, there is a family of estimators ${\hat\vartheta}_\alpha$, for $\alpha>0$, of the extremal coefficient, based on a transform of the absolute difference of the $\alpha$ power of the ranks. In the case of general bivariate copulas, we obtain the probability limit $\zeta_\alpha$ of $\hat{\zeta}_\alpha=2-{\hat\vartheta}_\alpha$ as the sample size goes to infinity, and show that (i) $\zeta_\alpha$ for $\alpha=1$ is a measure of central dependence with properties similar to Kendall's tau and Spearman's rank correlation, (ii) $\zeta_\alpha$ is a tail-weighted dependence measure for large $\alpha$, and (iii) the limit as $\alpha\to\infty$ is the upper tail dependence coefficient. We obtain asymptotic properties for the rank-based measure ${\hat\zeta}_\alpha$, and estimate tail dependence coefficients through extrapolation on ${\hat\zeta}_\alpha$. A data example illustrates the use of the new dependence measures for tail inference.-
dc.languageeng-
dc.publisherTaylor & Francis. The Journal's web site is located at http://www.tandf.co.uk/journals/titles/10485252.asp-
dc.relation.ispartofJournal of Nonparametric Statistics-
dc.rightsThis is an electronic version of an article published in [include the complete citation information for the final version of the article as published in the print edition of the journal]. [JOURNAL TITLE] is available online at: http://www.informaworld.com/smpp/ with the open URL of your article.-
dc.titleTail-weighted dependence measures with limit being the tail dependence coefficient-
dc.typeArticle-
dc.identifier.emailLee, D: leedav@hku.hk-
dc.identifier.authorityLee, D=rp02276-
dc.identifier.doi10.1080/10485252.2017.1407414-
dc.identifier.hkuros288844-
dc.identifier.volume30-
dc.identifier.spage262-
dc.identifier.epage290-