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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

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.

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

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    9. 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:

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    3. Marta Cousido-Rocha & Jacobo Uña-Álvarez & Jeffrey D. Hart, 2019. "Testing equality of a large number of densities under mixing conditions," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(4), pages 1203-1228, December.
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