Tail Dependence Matrices and Tests Based on Spearman's ρ and Kendall's τ  

作　　者：Lingyue Zhang Dawei Lu Hengjian Cui 

机构地区：[1]School of Mathematical Sciences,Capital Normal University,Beijing 100048,P.R.China [2]School of Mathematical Sciences,Dalian University of Technology,Dalian 116024,P.R.China

出　　处：《Acta Mathematica Sinica,English Series》2025年第2期522-546,共25页数学学报(英文版)

基　　金：Supported by the State Key Program of the National Natural Science Foundation of China (Grant No. 12031016);National Natural Science Foundation of China (Grant Nos. 11971324, 11901406, 12201435);Beijing Postdoctoral Research Foundation (Grant No. 2022-ZZ-084);Dalian High-level Talent Innovation Project (Grant No.2020RD09);the Interdisciplinary Construction of Bioinformatics and Statistics;the Academy for Multidisciplinary Studies;Capital Normal University

摘　　要：Measuring and testing tail dependence is important in finance, insurance, and risk management. This paper proposes two tail dependence matrices based on classic rank correlation coefficients,which possess the desired population properties and interpretability. Their nonparametric estimators with strong consistency and asymptotic distributions are derived using the limit theory of U-processes.The simulation and application studies show that, compared to the tail dependence matrix based on Spearman's ρ with large deviation, the Kendall-based tail dependence measure has stable variances under different tail conditions;thus, it is an effective approach to testing and quantifying tail dependence between random variables.

关 键 词：Tail dependence Spearman's Kendall's -statistic COPULA 

分 类 号：O212.1[理学—概率论与数理统计]