A new class of measures of bivariate tail dependence called tail concordance measures (TCMs) is proposed, which is defined as the limit of a measure of concordance of the underlying copula restricted to the tail region of interest. TCMs captures the extremal relationship between random variables not only along the diagonal but also along all angles weighted by a tail generating measure. Axioms of tail dependence measures are introduced, and TCMs are shown to characterize linear tail dependence measures. The infimum and supremum of TCMs over all generating measures are considered to investigate the issue of under- and overestimation of the degree of extreme co-movements. The infimum is shown to be attained by the classical tail dependence coefficient, and thus the classical notion always underestimates the degree of tail dependence. A formula for the supremum TCM is derived and shown to overestimate the degree of extreme co-movements. Estimators of the proposed measures are studied, and their performance is demonstrated in numerical experiments. For a fair assessment of tail dependence and stability of the estimation under small sample sizes, TCMs weighted over all angles are suggested, with tail Spearman's rho and tail Gini's gamma being interesting novel special cases of TCMs.

翻译：提出了新型双轨尾鱼依赖性衡量标准,称为尾巴协调措施(TCMS),其定义是,限制仅限尾尾部感兴趣的尾部区域对底部相交点的调和度; 三角措施不仅捕捉了沿对角线随机变量之间的极端关系,而且捕捉了按尾尾部生成量加权的所有角度的随机变量之间的极端关系; 引入了尾尾部依赖性衡量标准,并展示了尾部依赖性衡量标准对线性尾部依赖性衡量标准的特点; 认为TCM对所有生成措施的刺激和超额衡量标准进行了研究,以调查极端共移动程度的估测度不足和过高的问题; 典型尾部依赖性系数显示为典型尾部依赖系数所达到的最基本关系,因此传统概念总是低估尾部依赖性的程度; 尾部依赖性依赖性计量的公式被推导出,并显示高估了极端尾部依赖性衡量标准的程度; 研究了拟议措施的刺激因素,并在数字实验中展示了其性表现; 对尾部依赖性和过度性估计的尾部和尾部尾部尾部分析,建议的所有尾部为新型尾部。