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Cramér–von Mises and characteristic function tests for the two and k-sample problems with dependent data


  • Quessy, Jean-François
  • Éthier, François


Statistical procedures for the equality of two and k univariate distributions based on samples of dependent observations are proposed in this work. The test statistics are L2 distances of standard empirical and characteristic function processes. The p-values of the tests are obtained from a version of the multiplier central limit theorem whose asymptotic validity is established. Simple formulas for the test statistics and their multiplier versions in terms of multiplication of matrices are provided. Simulations under many patterns of dependence characterized by copulas show the good behavior of the tests in small samples, both in terms of their power and of their ability to keep their nominal level under the null hypothesis.

Suggested Citation

  • Quessy, Jean-François & Éthier, François, 2012. "Cramér–von Mises and characteristic function tests for the two and k-sample problems with dependent data," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 2097-2111.
  • Handle: RePEc:eee:csdana:v:56:y:2012:i:6:p:2097-2111 DOI: 10.1016/j.csda.2011.12.021

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    References listed on IDEAS

    1. Rémillard, Bruno & Scaillet, Olivier, 2009. "Testing for equality between two copulas," Journal of Multivariate Analysis, Elsevier, vol. 100(3), pages 377-386, March.
    2. Bajorunaite, Ruta & Klein, John P., 2007. "Two-sample tests of the equality of two cumulative incidence functions," Computational Statistics & Data Analysis, Elsevier, vol. 51(9), pages 4269-4281, May.
    3. John, Majnu & Priebe, Carey E., 2007. "A data-adaptive methodology for finding an optimal weighted generalized Mann-Whitney-Wilcoxon statistic," Computational Statistics & Data Analysis, Elsevier, vol. 51(9), pages 4337-4353, May.
    4. Christian Genest & Johanna Nešlehová & Jean-François Quessy, 2012. "Tests of symmetry for bivariate copulas," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(4), pages 811-834, August.
    5. Neubert, Karin & Brunner, Edgar, 2007. "A studentized permutation test for the non-parametric Behrens-Fisher problem," Computational Statistics & Data Analysis, Elsevier, vol. 51(10), pages 5192-5204, June.
    6. Burke, Murray D., 2000. "Multivariate tests-of-fit and uniform confidence bands using a weighted bootstrap," Statistics & Probability Letters, Elsevier, vol. 46(1), pages 13-20, January.
    7. Zhang, Jin & Wu, Yuehua, 2007. "k-Sample tests based on the likelihood ratio," Computational Statistics & Data Analysis, Elsevier, vol. 51(9), pages 4682-4691, May.
    8. Jean-François Quessy, 2012. "Testing for Bivariate Extreme Dependence Using Kendall's Process," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 39(3), pages 497-514, September.
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    Cited by:

    1. Ghanem, Dalia, 2017. "Testing identifying assumptions in nonseparable panel data models," Journal of Econometrics, Elsevier, vol. 197(2), pages 202-217.
    2. Jiménez-Gamero, M.D. & Alba-Fernández, M.V. & Jodrá, P. & Barranco-Chamorro, I., 2017. "Fast tests for the two-sample problem based on the empirical characteristic function," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 137(C), pages 390-410.
    3. Meintanis, Simos G. & Ushakov, Nikolai G., 2016. "Nonparametric probability weighted empirical characteristic function and applications," Statistics & Probability Letters, Elsevier, vol. 108(C), pages 52-61.


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