Tests of independence and randomness based on the empirical copula process
Tests of independence and randomness based on the empirical copula process
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DOI：
10.1007/bf02595777
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发表时间：
2004-12-01
期刊：
影响因子：
1.3
通讯作者：
Rémillard, B
中科院分区：
文献类型：
--
作者：
Genest, C;Rémillard, B
Deheuveles(1981a)描述了将经验Copula过程分解成有限个渐近相互独立的子过程，在多元分布等于其边际的乘积的假设下，这些子过程的联合极限分布是容易处理的。证明了这一结果可以推广到序列情形，并且极限过程具有与非序列情形相同的联合分布。因此，线性秩统计量在这两种情况下具有相同的渐近分布。它还展示了如何利用这些事实来构造简单的统计量，以图形化地检测依赖关系并对其进行形式化测试。模拟被用来探索这些统计量的有限样本行为，这些统计量被发现对各种类型的替代方案具有强大的能力。
Deheuvels (1981a) described a decomposition of the empirical copula process into a finite number of asymptotically mutually independent sub-processes whose joint limiting distribution is tractable under the hypothesis that a multivariate distribution is equal to the product of its margins. It is proved here that this result can be extended to the serial case and that the limiting processes have the same joint distribution as in the non-serial setting. As a consequence, linear rank statistics have the same asymptotic distribution in both contexts. It is also shown how these facts can be exploited to construct simple statistics for detecting dependence graphically and testing it formally. Simulations are used to explore the finite-sample behavior of these statistics, which are found to be powerful against various types of alternatives.