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

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  • Quessy, Jean-François
  • Éthier, François
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    Abstract

    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.

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    File URL: http://www.sciencedirect.com/science/article/pii/S0167947311004567
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    Bibliographic Info

    Article provided by Elsevier in its journal Computational Statistics & Data Analysis.

    Volume (Year): 56 (2012)
    Issue (Month): 6 ()
    Pages: 2097-2111

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    Handle: RePEc:eee:csdana:v:56:y:2012:i:6:p:2097-2111

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    Web page: http://www.elsevier.com/locate/csda

    Related research

    Keywords: Characteristic function; Copula; Dependent data; Empirical processes; Multiplier central limit theorem; Two and k-sample problems;

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    1. 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.
    2. Christian Genest & Johanna Nešlehová & Jean-François Quessy, 2012. "Tests of symmetry for bivariate copulas," Annals of the Institute of Statistical Mathematics, Springer, vol. 64(4), pages 811-834, August.
    3. 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.
    4. Bruno Rémillard & Olivier Scaillet, 2006. "Testing For Equality Between Two Copulas," Swiss Finance Institute Research Paper Series 07-24, Swiss Finance Institute.
    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. 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.
    7. 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, 09.
    8. 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.
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