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Article: Tailweighted dependence measures with limit being the tail dependence coefficient
Title  Tailweighted dependence measures with limit being the tail dependence coefficient 

Authors  
Issue Date  2018 
Publisher  Taylor & Francis. The Journal's web site is located at http://www.tandf.co.uk/journals/titles/10485252.asp 
Citation  Journal of Nonparametric Statistics, 2018, v. 30, p. 262290 How to Cite? 
Abstract  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 tailweighted 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 rankbased 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. 
Persistent Identifier  http://hdl.handle.net/10722/259500 
DC Field  Value  Language 

dc.contributor.author  Lee, D   
dc.contributor.author  Joe, H   
dc.contributor.author  Krupskii, P   
dc.date.accessioned  20180903T04:08:50Z   
dc.date.available  20180903T04:08:50Z   
dc.date.issued  2018   
dc.identifier.citation  Journal of Nonparametric Statistics, 2018, v. 30, p. 262290   
dc.identifier.uri  http://hdl.handle.net/10722/259500   
dc.description.abstract  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 tailweighted 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 rankbased 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.language  eng   
dc.publisher  Taylor & Francis. The Journal's web site is located at http://www.tandf.co.uk/journals/titles/10485252.asp   
dc.relation.ispartof  Journal of Nonparametric Statistics   
dc.rights  This 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.title  Tailweighted dependence measures with limit being the tail dependence coefficient   
dc.type  Article   
dc.identifier.email  Lee, D: leedav@hku.hk   
dc.identifier.authority  Lee, D=rp02276   
dc.identifier.doi  10.1080/10485252.2017.1407414   
dc.identifier.hkuros  288844   
dc.identifier.volume  30   
dc.identifier.spage  262   
dc.identifier.epage  290   