Tests of independence among continuous random vectors based on Cramér-von Mises functionals of the empirical copula process

Authors:
Ivan Kojadinovic;Mark Holmes
Affiliations:
Department of Statistics, The University of Auckland, Private Bag 92019, Auckland 1142, New Zealand;Department of Statistics, The University of Auckland, Private Bag 92019, Auckland 1142, New Zealand
Venue:
Journal of Multivariate Analysis
Year:
2009

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Abstract

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.