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A multivariate empirical characteristic function test of independence with normal marginals

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  • Bilodeau, M.
  • Lafaye de Micheaux, P.

Abstract

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 Cramer-von 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 Cramer-von Mises functionals is approximated by the Cornish-Fisher 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.

Suggested Citation

  • Bilodeau, M. & Lafaye de Micheaux, P., 2005. "A multivariate empirical characteristic function test of independence with normal marginals," Journal of Multivariate Analysis, Elsevier, vol. 95(2), pages 345-369, August.
  • Handle: RePEc:eee:jmvana:v:95:y:2005:i:2:p:345-369
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    References listed on IDEAS

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    1. Deheuvels, Paul, 1981. "An asymptotic decomposition for multivariate distribution-free tests of independence," Journal of Multivariate Analysis, Elsevier, vol. 11(1), pages 102-113, March.
    2. Henze, Norbert & Wagner, Thorsten, 1997. "A New Approach to the BHEP Tests for Multivariate Normality," Journal of Multivariate Analysis, Elsevier, vol. 62(1), pages 1-23, July.
    3. Ghoudi, Kilani & Kulperger, Reg J. & Rémillard, Bruno, 2001. "A Nonparametric Test of Serial Independence for Time Series and Residuals," Journal of Multivariate Analysis, Elsevier, vol. 79(2), pages 191-218, November.
    4. Kellermeier, John, 1980. "The empirical characteristic function and large sample hypothesis testing," Journal of Multivariate Analysis, Elsevier, vol. 10(1), pages 78-87, March.
    5. L. Baringhaus & N. Henze, 1988. "A consistent test for multivariate normality based on the empirical characteristic function," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 35(1), pages 339-348, December.
    6. Csörgo, Sándor, 1985. "Testing for independence by the empirical characteristic function," Journal of Multivariate Analysis, Elsevier, vol. 16(3), pages 290-299, June.
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    Cited by:

    1. Jiang, Qing & Hušková, Marie & Meintanis, Simos G. & Zhu, Lixing, 2019. "Asymptotics, finite-sample comparisons and applications for two-sample tests with functional data," Journal of Multivariate Analysis, Elsevier, vol. 170(C), pages 202-220.
    2. Simos G. Meintanis & Joseph Ngatchou-Wandji & James Allison, 2018. "Testing for serial independence in vector autoregressive models," Statistical Papers, Springer, vol. 59(4), pages 1379-1410, December.
    3. Jin, Ze & Matteson, David S., 2018. "Generalizing distance covariance to measure and test multivariate mutual dependence via complete and incomplete V-statistics," Journal of Multivariate Analysis, Elsevier, vol. 168(C), pages 304-322.
    4. Meintanis, Simos G. & Iliopoulos, George, 2008. "Fourier methods for testing multivariate independence," Computational Statistics & Data Analysis, Elsevier, vol. 52(4), pages 1884-1895, January.
    5. Fan, Yanan & de Micheaux, Pierre Lafaye & Penev, Spiridon & Salopek, Donna, 2017. "Multivariate nonparametric test of independence," Journal of Multivariate Analysis, Elsevier, vol. 153(C), pages 189-210.
    6. Hlávka, Zdenek & Husková, Marie & Meintanis, Simos G., 2011. "Tests for independence in non-parametric heteroscedastic regression models," Journal of Multivariate Analysis, Elsevier, vol. 102(4), pages 816-827, April.
    7. Chen, Feifei & Meintanis, Simos G. & Zhu, Lixing, 2019. "On some characterizations and multidimensional criteria for testing homogeneity, symmetry and independence," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 125-144.
    8. Beran, R. & Bilodeau, M. & Lafaye de Micheaux, P., 2007. "Nonparametric tests of independence between random vectors," Journal of Multivariate Analysis, Elsevier, vol. 98(9), pages 1805-1824, October.

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