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Testing equality of a large number of densities under mixing conditions

Author

Listed:
  • Marta Cousido-Rocha

    (University of Vigo
    University of Vigo)

  • Jacobo Uña-Álvarez

    (University of Vigo
    University of Vigo)

  • Jeffrey D. Hart

    (Texas A&M University)

Abstract

In certain settings, such as microarray data, the sampling information is formed by a large number of possibly dependent small data sets. In special applications, for example in order to perform clustering, the researcher aims to verify whether all data sets have a common distribution. For this reason we propose a formal test for the null hypothesis that all data sets come from a single distribution. The asymptotic setting is that in which the number of small data sets goes to infinity, while the sample size remains fixed. The asymptotic null distribution of the proposed test is derived under mixing conditions on the sequence of small data sets, and the power properties of our test under two reasonable fixed alternatives are investigated. A simulation study is conducted, showing that the test respects the nominal level, and that it has a power which tends to 1 when the number of data sets tends to infinity. An illustration involving microarray data is provided.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:testjl:v:28:y:2019:i:4:d:10.1007_s11749-018-00625-3
    DOI: 10.1007/s11749-018-00625-3
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    References listed on IDEAS

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    1. 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.
    2. D. Zhan & J. D. Hart, 2014. "Testing equality of a large number of densities," Biometrika, Biometrika Trust, vol. 101(2), pages 449-464.
    3. Dehling, Herold & Wendler, Martin, 2010. "Central limit theorem and the bootstrap for U-statistics of strongly mixing data," Journal of Multivariate Analysis, Elsevier, vol. 101(1), pages 126-137, January.
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    Cited by:

    1. Cousido-Rocha, Marta & de Uña-Álvarez, Jacobo & Hart, Jeffrey D., 2019. "A two-sample test for the equality of univariate marginal distributions for high-dimensional data," Journal of Multivariate Analysis, Elsevier, vol. 174(C).
    2. M. D. Jiménez-Gamero & M. Cousido-Rocha & M. V. Alba-Fernández & F. Jiménez-Jiménez, 2022. "Testing the equality of a large number of populations," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(1), pages 1-21, March.
    3. Jiménez-Gamero, M. Dolores & Franco-Pereira, Alba M., 2021. "Testing the equality of a large number of means of functional data," Journal of Multivariate Analysis, Elsevier, vol. 185(C).

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