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Nonparametric confidence intervals for ranked set samples

Author

Listed:
  • Santu Ghosh

    (Augusta University)

  • Arpita Chatterjee

    (Georgia Southern University)

  • N. Balakrishnan

    (McMaster University)

Abstract

In this work, we propose several different confidence interval methods based on ranked-set samples. First, we develop bootstrap bias-corrected and accelerated method for constructing confidence intervals based on ranked-set samples. Usually, for this method, the accelerated constant is computed by employing jackknife method. Here, we derive an analytical expression for the accelerated constant, which results in reducing the computational burden of this bias-corrected and accelerated bootstrap method. The other proposed confidence interval approaches are based on a monotone transformation along with normal approximation. We also study the asymptotic properties of the proposed methods. The performances of these methods are then compared with those of the conventional methods. Through this empirical study, it is shown that the proposed confidence intervals can be successfully applied in practice. The usefulness of the proposed methods is further illustrated by analyzing a real-life data on shrubs.

Suggested Citation

  • Santu Ghosh & Arpita Chatterjee & N. Balakrishnan, 2017. "Nonparametric confidence intervals for ranked set samples," Computational Statistics, Springer, vol. 32(4), pages 1689-1725, December.
    • Handle: RePEc:spr:compst:v:32:y:2017:i:4:d:10.1007_s00180-017-0744-0
    DOI: 10.1007/s00180-017-0744-0
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    References listed on IDEAS

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    1. Daniel F. Linder & Hani Samawi & Lili Yu & Arpita Chatterjee & Yisong Huang & Robert Vogel, 2015. "On stratified bivariate ranked set sampling for regression estimators," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(12), pages 2571-2583, December.
    2. Hani M. Samawi & Haresh Rochani & Daniel Linder & Arpita Chatterjee, 2017. "More efficient logistic analysis using moving extreme ranked set sampling," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(4), pages 753-766, March.
    3. Haiying Chen & Elizabeth A. Stasny & Douglas A. Wolfe, 2006. "Unbalanced Ranked Set Sampling for Estimating a Population Proportion," Biometrics, The International Biometric Society, vol. 62(1), pages 150-158, March.
    4. Modarres, Reza & Hui, Terrence P. & Zheng, Gang, 2006. "Resampling methods for ranked set samples," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 1039-1050, November.
    5. Fligner, Michael A. & MacEachern, Steven N., 2006. "Nonparametric Two-Sample Methods for Ranked-Set Sample Data," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1107-1118, September.
    6. Omer Ozturk & N. Balakrishnan, 2009. "An Exact Control-Versus-Treatment Comparison Test Based on Ranked Set Samples," Biometrics, The International Biometric Society, vol. 65(4), pages 1213-1222, December.
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