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Empirical likelihood for the two-sample mean problem

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  • Liu, Yukun
  • Zou, Changliang
  • Zhang, Runchu
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    Abstract

    We apply empirical likelihood method to constructing confidence regions for the difference of the means of two d-dimensional samples. It is shown that the empirical likelihood ratio test has an asymptotic chi-squared distribution. The Bartlett correction for the univariate case (d=1) has been investigated by Jing [1995. Two-sample empirical likelihood method. Statist. Probab. Lett. 24, 315-319]. Unfortunately, the Bartlett correction obtained in that article was incorrect. In this article the correct Bartlett correction is found and its effectiveness is shown by a simulation study.

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    Bibliographic Info

    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 78 (2008)
    Issue (Month): 5 (April)
    Pages: 548-556

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    Handle: RePEc:eee:stapro:v:78:y:2008:i:5:p:548-556

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    Keywords: Empirical likelihood Bartlett correction Coverage accuracy Two-sample problem;

    References

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    1. Song Chen, 1993. "On the accuracy of empirical likelihood confidence regions for linear regression model," Annals of the Institute of Statistical Mathematics, Springer, vol. 45(4), pages 621-637, December.
    2. Jing, Bing-Yi, 1995. "Two-sample empirical likelihood method," Statistics & Probability Letters, Elsevier, vol. 24(4), pages 315-319, September.
    3. Chen, S. X., 1994. "Empirical Likelihood Confidence Intervals for Linear Regression Coefficients," Journal of Multivariate Analysis, Elsevier, vol. 49(1), pages 24-40, April.
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    Cited by:
    1. Wu, Fan & Tsao, Min, 2014. "Two-sample extended empirical likelihood," Statistics & Probability Letters, Elsevier, vol. 84(C), pages 81-87.
    2. Liu, Yukun & Yu, Chi Wai, 2010. "Bartlett correctable two-sample adjusted empirical likelihood," Journal of Multivariate Analysis, Elsevier, vol. 101(7), pages 1701-1711, August.
    3. Gong, Yun & Peng, Liang & Qi, Yongcheng, 2010. "Smoothed jackknife empirical likelihood method for ROC curve," Journal of Multivariate Analysis, Elsevier, vol. 101(6), pages 1520-1531, July.

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