Tail-weighted dependence measures with limit being the tail dependence coefficient

Handle URI:
http://hdl.handle.net/10754/626608
Title:
Tail-weighted dependence measures with limit being the tail dependence coefficient
Authors:
Lee, David ( 0000-0001-9957-233X ) ; Joe, Harry; Krupskii, Pavel
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 (Formula presented.), for (Formula presented.), of the extremal coefficient, based on a transform of the absolute difference of the α power of the ranks. In the case of general bivariate copulas, we obtain the probability limit (Formula presented.) of (Formula presented.) as the sample size goes to infinity and show that (i) (Formula presented.) for (Formula presented.) is a measure of central dependence with properties similar to Kendall's tau and Spearman's rank correlation, (ii) (Formula presented.) is a tail-weighted dependence measure for large α, and (iii) the limit as (Formula presented.) is the upper tail dependence coefficient. We obtain asymptotic properties for the rank-based measure (Formula presented.) and estimate tail dependence coefficients through extrapolation on (Formula presented.). A data example illustrates the use of the new dependence measures for tail inference.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Citation:
Lee D, Joe H, Krupskii P (2017) Tail-weighted dependence measures with limit being the tail dependence coefficient. Journal of Nonparametric Statistics: 1–29. Available: http://dx.doi.org/10.1080/10485252.2017.1407414.
Publisher:
Informa UK Limited
Journal:
Journal of Nonparametric Statistics
Issue Date:
2-Dec-2017
DOI:
10.1080/10485252.2017.1407414
Type:
Article
ISSN:
1048-5252; 1029-0311
Sponsors:
The authors would like to thank the anonymous referees for their useful comments and suggestions.
Additional Links:
http://www.tandfonline.com/doi/full/10.1080/10485252.2017.1407414
Appears in Collections:
Articles; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorLee, Daviden
dc.contributor.authorJoe, Harryen
dc.contributor.authorKrupskii, Pavelen
dc.date.accessioned2018-01-01T12:19:02Z-
dc.date.available2018-01-01T12:19:02Z-
dc.date.issued2017-12-02en
dc.identifier.citationLee D, Joe H, Krupskii P (2017) Tail-weighted dependence measures with limit being the tail dependence coefficient. Journal of Nonparametric Statistics: 1–29. Available: http://dx.doi.org/10.1080/10485252.2017.1407414.en
dc.identifier.issn1048-5252en
dc.identifier.issn1029-0311en
dc.identifier.doi10.1080/10485252.2017.1407414en
dc.identifier.urihttp://hdl.handle.net/10754/626608-
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 (Formula presented.), for (Formula presented.), of the extremal coefficient, based on a transform of the absolute difference of the α power of the ranks. In the case of general bivariate copulas, we obtain the probability limit (Formula presented.) of (Formula presented.) as the sample size goes to infinity and show that (i) (Formula presented.) for (Formula presented.) is a measure of central dependence with properties similar to Kendall's tau and Spearman's rank correlation, (ii) (Formula presented.) is a tail-weighted dependence measure for large α, and (iii) the limit as (Formula presented.) is the upper tail dependence coefficient. We obtain asymptotic properties for the rank-based measure (Formula presented.) and estimate tail dependence coefficients through extrapolation on (Formula presented.). A data example illustrates the use of the new dependence measures for tail inference.en
dc.description.sponsorshipThe authors would like to thank the anonymous referees for their useful comments and suggestions.en
dc.publisherInforma UK Limiteden
dc.relation.urlhttp://www.tandfonline.com/doi/full/10.1080/10485252.2017.1407414en
dc.subjectCopulaen
dc.subjectextremal coefficienten
dc.subjectmonotone dependenceen
dc.subjecttail orderen
dc.subjecttail-weighted dependenceen
dc.titleTail-weighted dependence measures with limit being the tail dependence coefficienten
dc.typeArticleen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.identifier.journalJournal of Nonparametric Statisticsen
dc.contributor.institutionDepartment of Statistics, University of British Columbia, Vancouver, British Columbia, Canadaen
kaust.authorKrupskii, Pavelen
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