Conditional copulas, association measures and their applications
Conditional copulas, association measures and their applications
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DOI：
10.1016/j.csda.2010.11.010
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发表时间：
2011-05-01
影响因子：
1.8
通讯作者：
Omelka, Marel
中科院分区：
文献类型：
--
作者：
Gijbels, Irene;Veraverbeke, Noel;Omelka, Marel
对依赖结构建模的一种方法是通过Copula函数，Copula函数是在变量的联合分布中捕获依赖结构的一种手段。关联测度如Kendall的tau或斯皮尔曼的rho可以表示为Copula的泛函。两个变量之间的相关性结构可能会受到协变量的高度影响，并且了解这种相关性结构如何随协变量所取的值而变化是真实的兴趣。这促使需要引入条件copula，以及相关的条件肯德尔的tau和斯皮尔曼的rho关联措施。在这些概念的介绍和动机之后，提出并讨论了条件copula的两个非参数估计。然后推导出条件关联测度的非参数估计。一个关键问题是，这些措施现在被视为协变量中的函数。所有估计的性能进行了研究，通过模拟研究，其中还包括一个数据驱动的算法选择平滑参数。两个真实的数据的例子说明了该方法的实用性。(C)2010 Elsevier B.V.保留所有权利。
One way to model a dependence structure is through the copula function which is a mean to capture the dependence structure in the joint distribution of variables. Association measures such as Kendall's tau or Spearman's rho can be expressed as functionals of the copula. The dependence structure between two variables can be highly influenced by a covariate, and it is of real interest to know how this dependence structure changes with the value taken by the covariate. This motivates the need for introducing conditional copulas, and the associated conditional Kendall's tau and Spearman's rho association measures. After the introduction and motivation of these concepts, two nonparametric estimators for a conditional copula are proposed and discussed. Then nonparametric estimates for the conditional association measures are derived. A key issue is that these measures are now looked at as functions in the covariate. The performances of all estimators are investigated via a simulation study which also includes a data-driven algorithm for choosing the smoothing parameters. The usefulness of the methods is illustrated on two real data examples. (C) 2010 Elsevier B.V. All rights reserved.