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

Cesar Augusto Taconeli () and Idemauro Antonio Rodrigues Lara
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Cesar Augusto Taconeli: Federal University of Paraná
Idemauro Antonio Rodrigues Lara: University of São Paulo

Computational Statistics, 2022, vol. 37, issue 5, No 9, 2267-2293

Abstract: 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).

Keywords: Anderson-Darling estimation; Double ranked set sampling; Maximum product of spacings; Monte Carlo simulation; Neoteric ranked set sampling; Paired ranked set sampling (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s00180-022-01198-4

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