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Short view Article in peer-reviewed journal
A multivariate empirical characteristic function test of independence with normal marginals
Bilodeau M. et al
Journal of Multivariate Analysis 95, 2 (2005) 345-369 - http://hal.archives-ouvertes.fr/hal-00299265
Martin Bilodeau ()1, Pierre Lafaye De Micheaux ()2, 3
1:  DMS - Département de mathématiques et de statistique
Université de Montréal
CP 6128 succ Centre-Ville Montréal QC H3C 3J7
2:  LJK - Laboratoire Jean Kuntzmann
CNRS : UMR5224 – Université Joseph Fourier - Grenoble I – Université Pierre-Mendès-France - Grenoble II – Institut Polytechnique de Grenoble - Grenoble Institute of Technology
Tour IRMA 51 rue des Mathématiques - 53 38041 GRENOBLE CEDEX 9
3:  GIN - U836 - Grenoble Institut des Neurosciences
INSERM : U836 – Université Joseph Fourier - Grenoble I – CHU Grenoble – CEA : DSV/IRTSV
UJF - Site Santé La Tronche - BP 170 - 38042 Grenoble Cedex 9
A multivariate empirical characteristic function test of independence with normal marginals
This paper proposes a semi-parametric test of independence (or serial independence) between marginal vectors each of which is normally distributed but without assuming the joint normality of these marginal vectors. The test statistic is a Cramér­von Mises functional of a process defined from the empirical characteristic function. This process is defined similarly as the process of Ghoudi et al. [J. Multivariate Anal. 79 (2001) 191] built from the empirical distribution function and used to test for independence between univariate marginal variables. The test statistic can be represented as a V-statistic. It is consistent to detect any form of dependence. The weak convergence of the process is derived. The asymptotic distribution of the Cramér­von Mises functionals is approximated by the Cornish­Fisher expansion using a recursive formula for cumulants and inversion of the characteristic function with numerical evaluation of the eigenvalues. The test statistic is finally compared with Wilks statistic for testing the parametric hypothesis of independence in the one-way MANOVA model with random effects.

Journal of Multivariate Analysis