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A Simple Density-Based Empirical Likelihood Ratio Test for Independence

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  • Albert Vexler
  • Wan-Min Tsai
  • Alan D. Hutson

Abstract

We develop a novel nonparametric likelihood ratio test for independence between two random variables using a technique that is free of the common constraints of defining a given set of specific dependence structures. Our methodology revolves around an exact density-based empirical likelihood ratio test statistic that approximates in a distribution-free fashion the corresponding most powerful parametric likelihood ratio test. We demonstrate that the proposed test is very powerful in detecting general structures of dependence between two random variables, including nonlinear and/or random-effect dependence structures. An extensive Monte Carlo study confirms that the proposed test is superior to the classical nonparametric procedures across a variety of settings. The real-world applicability of the proposed test is illustrated using data from a study of biomarkers associated with myocardial infarction. Supplementary materials for this article are available online.

Suggested Citation

  • Albert Vexler & Wan-Min Tsai & Alan D. Hutson, 2014. "A Simple Density-Based Empirical Likelihood Ratio Test for Independence," The American Statistician, Taylor & Francis Journals, vol. 68(3), pages 158-169, February.
    • Handle: RePEc:taf:amstat:v:68:y:2014:i:3:p:158-169
    DOI: 10.1080/00031305.2014.901922
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    References listed on IDEAS

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    1. Albert Vexler & Chengqing Wu, 2009. "An Optimal Retrospective Change Point Detection Policy," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(3), pages 542-558, September.
    2. Einmahl, J.H.J. & McKeague, I.W., 2002. "Empirical Likelihood based on Hypothesis Testing," Other publications TiSEM 402576fa-8c0e-45e2-a394-8, Tilburg University, School of Economics and Management.
    3. Mingliang Gu & Xiaoqun Dong & Xuezhi Zhang & Xumin Wang & Yue Qi & Jun Yu & Wenquan Niu, 2012. "Strong Association between Two Polymorphisms on 15q25.1 and Lung Cancer Risk: A Meta-Analysis," PLOS ONE, Public Library of Science, vol. 7(6), pages 1-8, June.
    4. Bian Wu & Hong-Li Liu & Sheng Zhang & Xiao-Rong Dong & Gang Wu, 2012. "Lack of an Association between Two BER Gene Polymorphisms and Breast Cancer Risk: A Meta-Analysis," PLOS ONE, Public Library of Science, vol. 7(12), pages 1-7, December.
    5. Nicole A. Lazar, 2003. "Bayesian empirical likelihood," Biometrika, Biometrika Trust, vol. 90(2), pages 319-326, June.
    6. Vexler, Albert & Gurevich, Gregory, 2010. "Empirical likelihood ratios applied to goodness-of-fit tests based on sample entropy," Computational Statistics & Data Analysis, Elsevier, vol. 54(2), pages 531-545, February.
    7. K. Klauer, 1986. "Non-exponential families of distributions," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 33(1), pages 299-305, December.
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    Cited by:

    1. Vexler, Albert & Zou, Li, 2022. "Linear projections of joint symmetry and independence applied to exact testing treatment effects based on multidimensional outcomes," Journal of Multivariate Analysis, Elsevier, vol. 190(C).
    2. Ćmiel, Bogdan & Ledwina, Teresa, 2020. "Validation of association," Insurance: Mathematics and Economics, Elsevier, vol. 91(C), pages 55-67.
    3. Hadi Alizadeh Noughabi & Albert Vexler, 2016. "An efficient correction to the density-based empirical likelihood ratio goodness-of-fit test for the inverse Gaussian distribution," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(16), pages 2988-3003, December.

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