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<p>Efficient and accurate estimation of population parameters is critical in modern data-driven research, especially when leveraging complex sampling designs. This paper introduces a novel ratio-cum-exponential <i>(RCE)</i> mean estimator that strategically integrates optimal auxiliary variables within various rational Ranked Set Sampling <i>(RSS)</i> frameworks, including Median <i>RSS (MRSS)</i>, Percentile <i>RSS (PRSS)</i>, and Except Extreme <i>RSS (EERSS)</i>. We rigorously derive the theoretical properties of the proposed estimator and conduct comprehensive simulation studies across symmetric and asymmetric population models to evaluate its performance. Additionally, the estimator’s practical utility is validated using a real-world dataset. Results demonstrate that the proposed estimator significantly outperforms existing classical and contemporary mean estimators by achieving substantial reductions in bias and mean squared error under diverse <i>RSS</i> schemes. This advancement offers a powerful tool for enhancing estimation efficiency in statistical sampling and sets a foundation for future research in optimal auxiliary information usage within <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(RSS\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="italic">RSS</mi> </mrow> </math></EquationSource> </InlineEquation>.</p>

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Enhancing Mean Estimation Accuracy Through Optimal Auxiliary Information in Rational Ranked Set Sampling

  • 期刊论文

  • 发表日期：

    2026年2月11日

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  • Alok Kumar,
  • R. R. Sinha

摘要

Efficient and accurate estimation of population parameters is critical in modern data-driven research, especially when leveraging complex sampling designs. This paper introduces a novel ratio-cum-exponential (RCE) mean estimator that strategically integrates optimal auxiliary variables within various rational Ranked Set Sampling (RSS) frameworks, including Median RSS (MRSS), Percentile RSS (PRSS), and Except Extreme RSS (EERSS). We rigorously derive the theoretical properties of the proposed estimator and conduct comprehensive simulation studies across symmetric and asymmetric population models to evaluate its performance. Additionally, the estimator’s practical utility is validated using a real-world dataset. Results demonstrate that the proposed estimator significantly outperforms existing classical and contemporary mean estimators by achieving substantial reductions in bias and mean squared error under diverse RSS schemes. This advancement offers a powerful tool for enhancing estimation efficiency in statistical sampling and sets a foundation for future research in optimal auxiliary information usage within \(RSS\) RSS .