期刊
JOURNAL OF MULTIVARIATE ANALYSIS
卷 100, 期 6, 页码 1137-1154出版社
ELSEVIER INC
DOI: 10.1016/j.jmva.2008.10.013
关键词
Empirical process; Mobius decomposition; Cramer-von Mises statistic; Bootstrap; Permutation
A decomposition of the independence empirical copula process into a finite number of asymptotically independent sub-processes was studied by Deheuvels. Starting from this decomposition, Genest and Remillard recently investigated tests of independence among random variables based on Cramer-von Mises statistics derived from the sub-processes. A generalization of Deheuvels' decomposition to the case where independence is to be tested among continuous random vectors is presented. The asymptotic behavior of the resulting collection of Cramer-von Mises statistics is derived. It is shown that they are not distribution-free. One way of carrying out the resulting tests of independence then involves using the bootstrap or the permutation methodology. The former is shown to behave consistently, while the latter is employed in practice. Finally, simulations are used to study the finite-sample behavior of the tests. (C) 2008 Elsevier Inc. All rights reserved.
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