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New Scheme of Empirical Likelihood Method for Ranked Set Sampling: Applications to Two One‐Sample Problems

Author

Listed:
  • Soohyun Ahn
  • Xinlei Wang
  • Chul Moon
  • Johan Lim

Abstract

We propose a novel empirical likelihood (EL) approach for ranked set sampling (RSS) that leverages the ranking structure and information of the RSS. Our new proposal suggests constraining the sum of the within‐stratum probabilities of each rank stratum to 1/H, where H is the number of rank strata. The use of the additional constraints eliminates the need of subjective weight selection in unbalanced RSS and facilitates a seamless extension of the method for balanced RSS to unbalanced RSS. We apply our new proposal to testing one sample population mean and evaluate its performance through a numerical study and two real‐world data sets, examining obesity from body fat data and symmetry of dental size from human tooth size data. We further consider the extension of the proposed EL method to jackknife EL.

Suggested Citation

  • Soohyun Ahn & Xinlei Wang & Chul Moon & Johan Lim, 2025. "New Scheme of Empirical Likelihood Method for Ranked Set Sampling: Applications to Two One‐Sample Problems," International Statistical Review, International Statistical Institute, vol. 93(3), pages 459-498, December.
    • Handle: RePEc:bla:istatr:v:93:y:2025:i:3:p:459-498
    DOI: 10.1111/insr.12589
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    References listed on IDEAS

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    1. Zhang, Zhengjia & Liu, Tianqing & Zhang, Baoxue, 2016. "Jackknife empirical likelihood inferences for the population mean with ranked set samples," Statistics & Probability Letters, Elsevier, vol. 108(C), pages 16-22.
    2. 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.
    3. Zhao, Yichuan & Su, Yueju & Yang, Hanfang, 2020. "Jackknife empirical likelihood inference for the Pietra ratio," Computational Statistics & Data Analysis, Elsevier, vol. 152(C).
    4. Xinlei Wang & Johan Lim & Lynne Stokes, 2008. "A Nonparametric Mean Estimator for Judgment Poststratified Data," Biometrics, The International Biometric Society, vol. 64(2), pages 355-363, June.
    5. Steven N. MacEachern & Ömer Öztürk & Douglas A. Wolfe & Gregory V. Stark, 2002. "A new ranked set sample estimator of variance," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(2), pages 177-188, May.
    6. Yongli Sang, 2021. "A Jackknife Empirical Likelihood Approach for Testing the Homogeneity of K Variances," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(7), pages 1025-1048, October.
    7. Xinlei Wang & Johan Lim & Lynne Stokes, 2016. "Using Ranked Set Sampling With Cluster Randomized Designs for Improved Inference on Treatment Effects," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(516), pages 1576-1590, October.
    8. Feng, Huijun & Peng, Liang, 2012. "Jackknife empirical likelihood tests for error distributions in regression models," Journal of Multivariate Analysis, Elsevier, vol. 112(C), pages 63-75.
    9. Ayman Baklizi, 2009. "Empirical likelihood intervals for the population mean and quantiles based on balanced ranked set samples," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 18(4), pages 483-505, November.
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