TY - JOUR

T1 - Tail-weighted dependence measures with limit being the tail dependence coefficient

AU - Lee, David

AU - Joe, Harry

AU - Krupskii, Pavel

N1 - KAUST Repository Item: Exported on 2020-10-01
Acknowledgements: The authors would like to thank the anonymous referees for their useful comments and suggestions.

PY - 2017/12/2

Y1 - 2017/12/2

N2 - 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.

AB - 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.

UR - http://hdl.handle.net/10754/626608

UR - http://www.tandfonline.com/doi/full/10.1080/10485252.2017.1407414

UR - http://www.scopus.com/inward/record.url?scp=85035799764&partnerID=8YFLogxK

U2 - 10.1080/10485252.2017.1407414

DO - 10.1080/10485252.2017.1407414

M3 - Article

SN - 1048-5252

VL - 30

SP - 262

EP - 290

JO - Journal of Nonparametric Statistics

JF - Journal of Nonparametric Statistics

IS - 2

ER -