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Improved confidence intervals based on ranked set sampling designs within a parametric bootstrap approach

Author

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  • Cesar Augusto Taconeli

    (Federal University of Paraná)

  • Idemauro Antonio Rodrigues Lara

    (University of São Paulo)

Abstract

We study the problem of obtaining confidence intervals (CIs) within a parametric framework under different ranked set sampling (RSS) designs. This is an important research issue since it has not yet been adequately addressed in the RSS literature. We focused on evaluating CIs based on a recently developed parametric bootstrap approach, and the asymptotic maximum likelihood CIs under simple random sampling (SRS) was taken as the counterpart. A comprehensive simulation study was carried out to evaluate the accuracy and precision of the CIs. We have considered as sampling designs the paired RSS, neoteric RSS, and double RSS, besides the original RSS and SRS. Different estimation methods and bootstrap CIs were evaluated. In addition, the robustness of the CIs to imperfect ranking was evaluated by inducing varied levels of ranking errors. The simulated results allowed us to identify accurate bootstrap CIs based on RSS and some of its extensions, which outperform the usual asymptotic or bootstrap CIs based on SRS in terms of accuracy (coverage rate) and/or precision (average width).

Suggested Citation

  • Cesar Augusto Taconeli & Idemauro Antonio Rodrigues Lara, 2022. "Improved confidence intervals based on ranked set sampling designs within a parametric bootstrap approach," Computational Statistics, Springer, vol. 37(5), pages 2267-2293, November.
    • Handle: RePEc:spr:compst:v:37:y:2022:i:5:d:10.1007_s00180-022-01198-4
    DOI: 10.1007/s00180-022-01198-4
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    References listed on IDEAS

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    1. Al-Saleh, M. Fraiwan & Al-Kadiri, M. Ali, 2000. "Double-ranked set sampling," Statistics & Probability Letters, Elsevier, vol. 48(2), pages 205-212, June.
    2. Anatolyev, Stanislav & Kosenok, Grigory, 2005. "An Alternative To Maximum Likelihood Based On Spacings," Econometric Theory, Cambridge University Press, vol. 21(2), pages 472-476, April.
    3. 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.
    4. Cesar Augusto Taconeli & Wagner Hugo Bonat, 2020. "On the performance of estimation methods under ranked set sampling," Computational Statistics, Springer, vol. 35(4), pages 1805-1826, December.
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