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Smoothed jackknife empirical likelihood for the difference of two quantiles

Author

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  • Hanfang Yang

    (Renmin University of China)

  • Yichuan Zhao

    (Georgia State University)

Abstract

In this paper, we propose a smoothed estimating equation for the difference of quantiles with two samples. Using the jackknife pseudo-sample technique for the estimating equation, we propose the jackknife empirical likelihood (JEL) ratio and establish the Wilk’s theorem. Due to avoiding estimating link variables, the simulation studies demonstrate that JEL method has computational efficiency compared with traditional normal approximation method. We carry out a simulation study in terms of coverage probability and average length of the proposed confidence intervals. A real data set is used to illustrate the JEL procedure.

Suggested Citation

  • Hanfang Yang & Yichuan Zhao, 2017. "Smoothed jackknife empirical likelihood for the difference of two quantiles," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 69(5), pages 1059-1073, October.
  • Handle: RePEc:spr:aistmt:v:69:y:2017:i:5:d:10.1007_s10463-016-0576-7
    DOI: 10.1007/s10463-016-0576-7
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    References listed on IDEAS

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    1. Jing, Bing-Yi & Yuan, Junqing & Zhou, Wang, 2009. "Jackknife Empirical Likelihood," Journal of the American Statistical Association, American Statistical Association, vol. 104(487), pages 1224-1232.
    2. Yang, Hanfang & Zhao, Yichuan, 2013. "Smoothed jackknife empirical likelihood inference for the difference of ROC curves," Journal of Multivariate Analysis, Elsevier, vol. 115(C), pages 270-284.
    3. Chen, Jian & Peng, Liang & Zhao, Yichuan, 2009. "Empirical likelihood based confidence intervals for copulas," Journal of Multivariate Analysis, Elsevier, vol. 100(1), pages 137-151, January.
    4. Vaart,A. W. van der, 2000. "Asymptotic Statistics," Cambridge Books, Cambridge University Press, number 9780521784504.
    5. Wang Zhou & Bing-Yi Jing, 2003. "Adjusted empirical likelihood method for quantiles," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 55(4), pages 689-703, December.
    6. 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.
    7. Yang, Hanfang & Zhao, Yichuan, 2015. "Smoothed jackknife empirical likelihood inference for ROC curves with missing data," Journal of Multivariate Analysis, Elsevier, vol. 140(C), pages 123-138.
    8. Liang Peng & Yongcheng Qi, 2010. "Smoothed jackknife empirical likelihood method for tail copulas," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 19(3), pages 514-536, November.
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    Cited by:

    1. Yang, Hanfang & Zhao, Yichuan, 2018. "Smoothed jackknife empirical likelihood for the one-sample difference of quantiles," Computational Statistics & Data Analysis, Elsevier, vol. 120(C), pages 58-69.
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    3. Yongcheng Qi, 2018. "Jackknife Empirical Likelihood Methods," Biostatistics and Biometrics Open Access Journal, Juniper Publishers Inc., vol. 7(2), pages 20-22, June.

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