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

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    Type
    Article
    Authors
    Lee, David cc
    Joe, Harry
    Krupskii, Pavel cc
    KAUST Department
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Date
    2017-12-02
    Online Publication Date
    2017-12-02
    Print Publication Date
    2018-04-03
    Permanent link to this record
    http://hdl.handle.net/10754/626608
    
    Metadata
    Show full item record
    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.
    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 Limited
    Journal
    Journal of Nonparametric Statistics
    DOI
    10.1080/10485252.2017.1407414
    Additional Links
    http://www.tandfonline.com/doi/full/10.1080/10485252.2017.1407414
    ae974a485f413a2113503eed53cd6c53
    10.1080/10485252.2017.1407414
    Scopus Count
    Collections
    Articles; Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division

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