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A NEW APPROACH TO ESTIMATION IN RANKED SET SAMPLING: SIMULATIONS AND A VARIETY OF APPLICATIONS
Keywords:
mean square error, simulation study, efficiency, auxiliary variableDOI:
https://doi.org/10.17654/0972361725062Abstract
In this paper, we introduce a novel class of estimators for estimating the population mean by incorporating information from an auxiliary variable within the framework of ranked set sampling (RSS). The key motivation behind this approach is to improve the accuracy and reliability of population mean estimation by leveraging additional, correlated information that an auxiliary variable can provide. To assess the performance of the proposed estimators, the mean square error (MSE) is derived analytically using a first-order approximation. This allows us to evaluate the bias and variance properties of the estimators, which are essential criteria for assessing estimator performance. Based on this analysis, the paper identifies specific conditions or efficiency requirements under which the proposed class outperforms conventional estimators - such as the simple mean estimator derived under simple random sampling (SRS) or traditional RSS-based methods. Positioned within the broader context of RSS, which integrates auxiliary information for efficient data collection, this approach addresses limitations in conventional estimators. The methodology involves analytically deriving the mean square error (MSE) using a first-order approximation to assess bias and variance properties. Results from extensive simulation studies using normal and exponential distributions reveal consistently lower MSEs compared to traditional methods, underscoring the enhanced efficiency and robustness of the proposed estimators. Additionally, real-world applications validate the practical utility and adaptability of this approach in diverse fields. By combining theoretical rigor with empirical validation, the proposed methodology significantly advances statistical estimation techniques, offering substantial improvements in precision and applicability.
Received: June 10, 2025
Revised: July 15, 2025
Accepted: August 2, 2025
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