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A test for equality of two distributions via jackknife empirical likelihood and characteristic functions

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  • Liu, Zhi
  • Xia, Xiaochao
  • Zhou, Wang

Abstract

The two-sample problem: testing the equality of two distributions is investigated. A jackknife empirical likelihood (JEL) test is proposed through incorporating characteristic functions, which reduces to a two-sample U-statistic. When the dimension of data is fixed, the nonparametric Wilks’s theorem for the proposed JEL ratio statistics is established. When the dimension diverges with the sample size at a moderate rate, p=o(n1/3), it is proved that under some mild conditions the normalized JEL ratio statistic has a standard normal limit. Moreover, when the dimension exceeds the sample size, p>n, an alternative version of JEL test is proposed. It is verified that under the null hypothesis this alternative version of JEL test has an asymptotical chi-squared distribution with two degrees of freedom. Some numerical results via simulation study and an analysis of a microarray dataset are presented and both confirm theoretical results empirically.

Suggested Citation

  • Liu, Zhi & Xia, Xiaochao & Zhou, Wang, 2015. "A test for equality of two distributions via jackknife empirical likelihood and characteristic functions," Computational Statistics & Data Analysis, Elsevier, vol. 92(C), pages 97-114.
    • Handle: RePEc:eee:csdana:v:92:y:2015:i:c:p:97-114
    DOI: 10.1016/j.csda.2015.06.004
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    References listed on IDEAS

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    1. Biswas, Munmun & Ghosh, Anil K., 2014. "A nonparametric two-sample test applicable to high dimensional data," Journal of Multivariate Analysis, Elsevier, vol. 123(C), pages 160-171.
    2. Chan, Ngai Hang & Chen, Song Xi & Peng, Liang & Yu, Cindy L., 2009. "Empirical Likelihood Methods Based on Characteristic Functions With Applications to Lévy Processes," Journal of the American Statistical Association, American Statistical Association, vol. 104(488), pages 1621-1630.
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    4. Zhenyu Liu & Reza Modarres, 2011. "A triangle test for equality of distribution functions in high dimensions," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 23(3), pages 605-615.
    5. Chen, Songxi, 2012. "Two Sample Tests for High Dimensional Covariance Matrices," MPRA Paper 46026, University Library of Munich, Germany.
    6. Chen, Song Xi & Qin, Yingli, 2010. "A Two Sample Test for High Dimensional Data with Applications to Gene-set Testing," MPRA Paper 59642, University Library of Munich, Germany.
    7. Song Xi Chen & Liang Peng & Ying-Li Qin, 2009. "Effects of data dimension on empirical likelihood," Biometrika, Biometrika Trust, vol. 96(3), pages 711-722.
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    Cited by:

    1. Xu Li & Wenjuan Hu & Baoxue Zhang, 2023. "Measuring and testing homogeneity of distributions by characteristic distance," Statistical Papers, Springer, vol. 64(2), pages 529-556, April.
    2. Zhang, Jin-Ting & Guo, Jia & Zhou, Bu, 2024. "Testing equality of several distributions in separable metric spaces: A maximum mean discrepancy based approach," Journal of Econometrics, Elsevier, vol. 239(2).
    3. Xu Chen & Fa-wen Li & Ping Feng, 2018. "Spatiotemporal variation of hydrological drought based on the Optimal Standardized Streamflow Index in Luanhe River basin, China," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 91(1), pages 155-178, March.
    4. 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).
    5. Yongli Sang & Xin Dang & Yichuan Zhao, 2020. "Depth-based weighted jackknife empirical likelihood for non-smooth U-structure equations," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(2), pages 573-598, June.
    6. Khan, Ruhul Ali, 2023. "Two-sample nonparametric test for proportional reversed hazards," Computational Statistics & Data Analysis, Elsevier, vol. 182(C).

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