IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v78y2008i5p548-556.html
   My bibliography  Save this article

Empirical likelihood for the two-sample mean problem

Author

Listed:
  • Liu, Yukun
  • Zou, Changliang
  • Zhang, Runchu

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.

Suggested Citation

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

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-7152(07)00286-6
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Chen, S. X., 1994. "Empirical Likelihood Confidence Intervals for Linear Regression Coefficients," Journal of Multivariate Analysis, Elsevier, vol. 49(1), pages 24-40, April.
    2. Song Chen, 1993. "On the accuracy of empirical likelihood confidence regions for linear regression model," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 45(4), pages 621-637, December.
    3. Jing, Bing-Yi, 1995. "Two-sample empirical likelihood method," Statistics & Probability Letters, Elsevier, vol. 24(4), pages 315-319, September.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. 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.
    3. Shen, Junshan & Yuen, Kam Chuen & Liu, Chunling, 2016. "Empirical likelihood confidence regions for one- or two- samples with doubly censored data," Computational Statistics & Data Analysis, Elsevier, vol. 93(C), pages 285-293.
    4. Tsao, Min & Wu, Fan, 2015. "Two-sample extended empirical likelihood for estimating equations," Journal of Multivariate Analysis, Elsevier, vol. 142(C), pages 1-15.
    5. Quynh Van Nong & Chi Tim Ng, 2021. "Clustering of subsample means based on pairwise L1 regularized empirical likelihood," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(1), pages 135-174, February.
    6. 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.
    7. Liang, Wei & Dai, Hongsheng & He, Shuyuan, 2019. "Mean Empirical Likelihood," Computational Statistics & Data Analysis, Elsevier, vol. 138(C), pages 155-169.
    8. Varron, Davit, 2016. "Empirical likelihood confidence tubes for functional parameters in plug-in estimation," Journal of Multivariate Analysis, Elsevier, vol. 152(C), pages 100-118.
    9. Apratim Guha & Atanu Biswas & Abhik Ghosh, 2021. "A nonparametric two‐sample test using a general φ‐divergence‐based mutual information," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 75(2), pages 180-202, May.
    10. Tsagris, Michail & Preston, Simon & T.A. Wood, Andrew, 2016. "Nonparametric hypothesis testing for equality of means on the simplex," MPRA Paper 72771, University Library of Munich, Germany.
    11. Wu, Fan & Tsao, Min, 2014. "Two-sample extended empirical likelihood," Statistics & Probability Letters, Elsevier, vol. 84(C), pages 81-87.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Xuemin Zi & Changliang Zou & Yukun Liu, 2012. "Two-sample empirical likelihood method for difference between coefficients in linear regression model," Statistical Papers, Springer, vol. 53(1), pages 83-93, February.
    3. Francesco Bravo, "undated". "Empirical likelihood specification testing in linear regression models," Discussion Papers 00/28, Department of Economics, University of York.
    4. Liang, Hua & Su, Haiyan & Zou, Guohua, 2008. "Confidence intervals for a common mean with missing data with applications in an AIDS study," Computational Statistics & Data Analysis, Elsevier, vol. 53(2), pages 546-553, December.
    5. Bruce Brown & Song Chen, 1998. "Combined and Least Squares Empirical Likelihood," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 50(4), pages 697-714, December.
    6. Wang, Qihua & Wang, Jane-Ling, 2001. "Inference for the Mean Difference in the Two-Sample Random Censorship Model," Journal of Multivariate Analysis, Elsevier, vol. 79(2), pages 295-315, November.
    7. Qin, Gengsheng & Jing, Bing-Yi, 2001. "Censored Partial Linear Models and Empirical Likelihood," Journal of Multivariate Analysis, Elsevier, vol. 78(1), pages 37-61, July.
    8. Cui, Hengjian & Chen, Song Xi, 2003. "Empirical likelihood confidence region for parameter in the errors-in-variables models," Journal of Multivariate Analysis, Elsevier, vol. 84(1), pages 101-115, January.
    9. Zhao, Yichuan & Chen, Feiming, 2008. "Empirical likelihood inference for censored median regression model via nonparametric kernel estimation," Journal of Multivariate Analysis, Elsevier, vol. 99(2), pages 215-231, February.
    10. Wang, Qi-Hua & Jing, Bing-Yi, 1999. "Empirical likelihood for partial linear models with fixed designs," Statistics & Probability Letters, Elsevier, vol. 41(4), pages 425-433, February.
    11. Jing, Bing-Yi, 1995. "Two-sample empirical likelihood method," Statistics & Probability Letters, Elsevier, vol. 24(4), pages 315-319, September.
    12. Wang, Qi-Hua & Li, Gang, 2002. "Empirical Likelihood Semiparametric Regression Analysis under Random Censorship," Journal of Multivariate Analysis, Elsevier, vol. 83(2), pages 469-486, November.
    13. Guo-Liang Fan & Han-Ying Liang & Jiang-Feng Wang, 2013. "Empirical likelihood for heteroscedastic partially linear errors-in-variables model with α-mixing errors," Statistical Papers, Springer, vol. 54(1), pages 85-112, February.
    14. Hu, Xuemei & Wang, Zhizhong & Zhao, Zhiwei, 2009. "Empirical likelihood for semiparametric varying-coefficient partially linear errors-in-variables models," Statistics & Probability Letters, Elsevier, vol. 79(8), pages 1044-1052, April.
    15. Ouyang, Jiangrong & Bondell, Howard, 2023. "Bayesian analysis of longitudinal data via empirical likelihood," Computational Statistics & Data Analysis, Elsevier, vol. 187(C).
    16. Chen, Xia & Cui, Hengjian, 2008. "Empirical likelihood inference for partial linear models under martingale difference sequence," Statistics & Probability Letters, Elsevier, vol. 78(17), pages 2895-2901, December.
    17. Lu, Wenbin & Liang, Yu, 2006. "Empirical likelihood inference for linear transformation models," Journal of Multivariate Analysis, Elsevier, vol. 97(7), pages 1586-1599, August.
    18. Shen, Junshan & Yuen, Kam Chuen & Liu, Chunling, 2016. "Empirical likelihood confidence regions for one- or two- samples with doubly censored data," Computational Statistics & Data Analysis, Elsevier, vol. 93(C), pages 285-293.
    19. Melnykov, Volodymyr & Shen, Gang, 2013. "Clustering through empirical likelihood ratio," Computational Statistics & Data Analysis, Elsevier, vol. 62(C), pages 1-10.
    20. Xue, Liu-Gen & Zhu, Lixing, 2006. "Empirical likelihood for single-index models," Journal of Multivariate Analysis, Elsevier, vol. 97(6), pages 1295-1312, July.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:stapro:v:78:y:2008:i:5:p:548-556. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.