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Empirical phi-divergence test statistics for the difference of means of two populations


  • N. Balakrishnan

    (McMaster University)

  • N. Martín

    () (Complutense University of Madrid)

  • L. Pardo

    (Complutense University of Madrid)


Abstract Empirical phi-divergence test statistics have demostrated to be a useful technique for the simple null hypothesis to improve the finite sample behavior of the classical likelihood ratio test statistic, as well as for model misspecification problems, in both cases for the one population problem. This paper introduces this methodology for two-sample problems. A simulation study illustrates situations in which the new test statistics become a competitive tool with respect to the classical z test and the likelihood ratio test statistic.

Suggested Citation

  • N. Balakrishnan & N. Martín & L. Pardo, 2017. "Empirical phi-divergence test statistics for the difference of means of two populations," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 101(2), pages 199-226, April.
  • Handle: RePEc:spr:alstar:v:101:y:2017:i:2:d:10.1007_s10182-017-0289-0
    DOI: 10.1007/s10182-017-0289-0

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    References listed on IDEAS

    1. Ayman Baklizi & B.M. Golam Kibria, 2009. "One and two sample confidence intervals for estimating the mean of skewed populations: an empirical comparative study," Journal of Applied Statistics, Taylor & Francis Journals, vol. 36(6), pages 601-609.
    2. Jing, Bing-Yi, 1995. "Two-sample empirical likelihood method," Statistics & Probability Letters, Elsevier, vol. 24(4), pages 315-319, September.
    3. A. Basu & A. Mandal & N. Martin & L. Pardo, 2015. "Robust tests for the equality of two normal means based on the density power divergence," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 78(5), pages 611-634, July.
    4. Liu, Yukun & Zou, Changliang & Zhang, Runchu, 2008. "Empirical likelihood for the two-sample mean problem," Statistics & Probability Letters, Elsevier, vol. 78(5), pages 548-556, April.
    5. B. M. Golam Kibria & Shipra Banik, 2013. "Parametric and nonparametric confidence intervals for estimating the difference of means of two skewed populations," Journal of Applied Statistics, Taylor & Francis Journals, vol. 40(12), pages 2617-2636, December.
    6. Philip Yu & Yijun Sun & Bimal Sinha, 2002. "Estimation of the Common Mean of a Bivariate Normal Population," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 54(4), pages 861-878, December.
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