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

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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).

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Acknowledgements

The authors thank the Editor and the Reviewers for their valuable comments on an earlier version of this manuscript.

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Authors and Affiliations

  1. Department of Statistics, Federal University of Paraná, Curitiba, Paraná, Brazil

    Cesar Augusto Taconeli

  2. Exact Sciencies Department, Luiz de Queiroz College of Agriculture, University of São Paulo, Piracicaba, São Paulo, Brazil

    Idemauro Antonio Rodrigues de Lara

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  1. Cesar Augusto Taconeli
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  2. Idemauro Antonio Rodrigues de Lara
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Correspondence to Cesar Augusto Taconeli.

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Taconeli, C.A., de Lara, I.A.R. Improved confidence intervals based on ranked set sampling designs within a parametric bootstrap approach. Comput Stat 37, 2267–2293 (2022). https://doi.org/10.1007/s00180-022-01198-4

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