On rank correlation measures for non-continuous random variables
On rank correlation measures for non-continuous random variables
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DOI：
10.1016/j.jmva.2005.11.007
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发表时间：
2007-03-01
影响因子：
1.6
通讯作者：
Neslehova, Johanna
中科院分区：
文献类型：
--
作者：
Neslehova, Johanna
对于连续型随机变量，许多相关概念和关联测度只能用相应的copula来表示，因此与边际分布无关。一旦边际分布函数出现不连续性，这种相互关系通常就会失效。本文考虑任意随机变量到均匀分布变量的一种变换。利用这种技术，在一般情况下，所有可能的copula类进行了研究。特别是，我们表明，它的成员之一，标准的扩展Copula介绍了Schweizer和Sklar捕获的依赖结构，以类似的方式独特的Copula在连续的情况下。此外，我们考虑任意随机变量之间的一致性的措施，并获得推广的肯德尔的τ和斯皮尔曼的ρ，对应于这些数量的样本版本的经验分布。(c)2006年爱思唯尔公司All rights reserved.
For continuous random variables, many dependence concepts and measures of association can be expressed in terms of the corresponding copula only and are thus independent of the marginal distributions. This interrelationship generally fails as soon as there are discontinuities in the marginal distribution functions. In this paper, we consider an alternative transformation of an arbitrary random variable to a uniformly distributed one. Using this technique, the class of all possible copulas in the general case is investigated. In particular, we show that one of its members-the standard extension copula introduced by Schweizer and Sklar-captures the dependence structures in an analogous way the unique copula does in the continuous case. Furthermore, we consider measures of concordance between arbitrary random variables and obtain generalizations of Kendall's tau and Spearman's rho that correspond to the sample version of these quantities for empirical distributions. (c) 2006 Elsevier Inc. All rights reserved.