Monotonicity of the tail dependence for multivariate t-copula  

多元t-copula尾相依的单调性(英文)

作　　者：石爱菊[1,2] 林金官[1] 

机构地区：[1]东南大学数学系,南京211189 [2]南京邮电大学理学院,南京210003

出　　处：《Journal of Southeast University(English Edition)》2011年第4期466-470,共5页东南大学学报（英文版）

基　　金：The National Natural Science Foundation of China(No.11001052,11171065);the National Science Foundation of Jiangsu Province(No.BK2011058);the Science Foundation of Nanjing University of Posts and Telecommunications(No.JG00710JX57)

摘　　要：This paper considers the upper orthant and extremal tail dependence indices for multivariate t-copula. Where, the multivariate t-copula is defined under a correlation structure. The explicit representations of the tail dependence parameters are deduced since the copula of continuous variables is invariant under strictly increasing transformation about the random variables, which are more simple than those obtained in previous research. Then, the local monotonicity of these indices about the correlation coefficient is discussed, and it is concluded that the upper extremal dependence index increases with the correlation coefficient, but the monotonicity of the upper orthant tail dependence index is complex. Some simulations are performed by the Monte Carlo method to verify the obtained results, which are found to be satisfactory. Meanwhile, it is concluded that the obtained conclusions can be extended to any distribution family in which the generating random variable has a regularly varying distribution.考虑了多元t-copula的上尾象限相依指数和上尾极值相依指数,该t-copula是在相依结构下定义的.由于多元连续型随机变量的copula函数关于严格单调递增变换具有不变性质,由此推导了多元t-copula的尾相依指数的精确表达式,得到的结果明显比以往文献给出的结论更加简洁.然后,讨论了这2个相依指数关于相关系数的局部单调性质:上尾极值相依指数关于相关系数是严格单调递增的,但上尾象限相依指数的单调性比较复杂.通过蒙特卡罗模拟数据验证了结果的正确性.同时,发现所有结论可以推广到生成随机变量是正则变化的分布类中.

关 键 词：multivariate t-copula COPULA inverse gamma distribution MONOTONICITY regularly varying function correlation coefficient 

分 类 号：O212.4[理学—概率论与数理统计]