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<p>The use of auxiliary or supplementary information plays a crucial role in enhancing the efficiency of estimators in survey sampling. Among various measures of central tendency, the median has attracted considerable attention due to its robustness against outliers and skewed distributions. This study introduces a novel estimator for the finite population median that incorporates supplementary information under a probability proportional to size (PPS) sampling design. Analytical expressions for the bias and mean squared error (MSE) of the proposed estimator are derived up to the first order of approximation. The efficiency of the proposed estimator is evaluated through theoretical comparisons and empirical analyses against existing median estimators, using MSE and percent relative efficiency (PRE) as performance criteria. Furthermore, graphical representations are employed to illustrate the comparative performance. The proposed estimator is examined using three real-world datasets, and its precision is further validated through a comprehensive simulation study. The findings consistently demonstrate that the proposed estimator outperforms its existing counterparts in terms of efficiency and robustness.</p>

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A new class of median estimators using auxiliary information under PPS sampling: theoretical properties and empirical evaluation

  • 期刊论文

  • 发表日期：

    2026年3月19日

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  • Salman Shah,
  • Eisa Mahmoudi,
  • Moiz Qureshi,
  • Hasnain Iftikhar,
  • Paulo Canas Rodrigues,
  • Ronny Ivan Gonzales Medina,
  • Javier Linkolk López-Gonzales

摘要

The use of auxiliary or supplementary information plays a crucial role in enhancing the efficiency of estimators in survey sampling. Among various measures of central tendency, the median has attracted considerable attention due to its robustness against outliers and skewed distributions. This study introduces a novel estimator for the finite population median that incorporates supplementary information under a probability proportional to size (PPS) sampling design. Analytical expressions for the bias and mean squared error (MSE) of the proposed estimator are derived up to the first order of approximation. The efficiency of the proposed estimator is evaluated through theoretical comparisons and empirical analyses against existing median estimators, using MSE and percent relative efficiency (PRE) as performance criteria. Furthermore, graphical representations are employed to illustrate the comparative performance. The proposed estimator is examined using three real-world datasets, and its precision is further validated through a comprehensive simulation study. The findings consistently demonstrate that the proposed estimator outperforms its existing counterparts in terms of efficiency and robustness.