Tests of independence among continuous random vectors based on Cramér-von Mises functionals of the empirical copula process. (English) Zbl 1159.62033
Summary: A decomposition of the independence empirical copula process into a finite number of asymptotically independent sub-processes was studied by P. Deheuvels [ibid. 11, 102–113 (1981; Zbl 0486.62043)]. Starting from this decomposition, C. Genest and B. Rémillard [Test 13, No. 2, 335–370 (2004; Zbl 1069.62039)] recently investigated tests of independence among random variables based on Cramér-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 Cramér-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.
MSC:
| 62G10 | Nonparametric hypothesis testing |
| 62H15 | Hypothesis testing in multivariate analysis |
| 62G20 | Asymptotic properties of nonparametric inference |
| 62G09 | Nonparametric statistical resampling methods |
Keywords:
empirical process; Möbius decomposition; Cramér-von Mises statistic; bootstrap; permutationReferences:
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