Tail-weighted dependence measures with limit being the tail dependence coefficient
Type
ArticleAuthors
Lee, David
Joe, Harry
Krupskii, Pavel

Date
2017-12-02Online Publication Date
2017-12-02Print Publication Date
2018-04-03Permanent link to this record
http://hdl.handle.net/10754/626608
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Show full item recordAbstract
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.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.Sponsors
The authors would like to thank the anonymous referees for their useful comments and suggestions.Publisher
Informa UK LimitedAdditional Links
http://www.tandfonline.com/doi/full/10.1080/10485252.2017.1407414ae974a485f413a2113503eed53cd6c53
10.1080/10485252.2017.1407414