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

Author

Listed:
  • Salman Shah

    (Yazd University, Department of Statistics)

  • Eisa Mahmoudi

    (Yazd University, Department of Statistics)

  • Moiz Qureshi

    (University of Sindh University, Department of Statistics
    Quaid-i-Azam University, Department of Statistics)

  • Hasnain Iftikhar

    (Quaid-i-Azam University, Department of Statistics
    University of Peshawar, Department of Statistics)

  • Paulo Canas Rodrigues

    (Federal University of Bahia, Department of Statistics
    University of Pretoria, Pretoria, Department of Business Management)

  • Ronny Ivan Gonzales Medina

    (Universidad Católica de Santa María, Facultad de Ciencias e Ingenierías Físicas y Formales)

  • Javier Linkolk López-Gonzales

    (Universidad Peruana Unión, Escuela de Posgrado)

Abstract

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.

Suggested Citation

  • Salman Shah & Eisa Mahmoudi & Moiz Qureshi & Hasnain Iftikhar & Paulo Canas Rodrigues & Ronny Ivan Gonzales Medina & Javier Linkolk López-Gonzales, 2026. "A new class of median estimators using auxiliary information under PPS sampling: theoretical properties and empirical evaluation," Computational Statistics, Springer, vol. 41(3), pages 1-25, April.
    • Handle: RePEc:spr:compst:v:41:y:2026:i:3:d:10.1007_s00180-026-01724-8
    DOI: 10.1007/s00180-026-01724-8
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    References listed on IDEAS

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    1. Garib Nath Singh & Ashok Kumar Jaiswal & Awadhesh K. Pandey, 2023. "Improved imputation methods for missing data in two-occasion successive sampling," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 52(6), pages 2010-2029, March.
    2. Sarjinder Singh, 2003. "Advanced Sampling Theory with Applications," Springer Books, Springer, number 978-94-007-0789-4, January.
    3. Sibel Aladag & Hulya Cingi, 2015. "Improvement in Estimating the Population Median in Simple Random Sampling and Stratified Random Sampling Using Auxiliary Information," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 44(5), pages 1013-1032, March.
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