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A new class of median estimators using auxiliary information under PPS sampling: theoretical properties and empirical evaluation
Author(s)
Shah, Salman
Yazd University
Mahmoudi, Eisa
Yazd University
Qureshi, Moiz
Quaid-i-Azam University
Iftikhar, Hasnain
Quaid-i-Azam University
Rodrigues, Paulo Canas
Universidade Federal da Bahia
Gonzales Medina, Ronny Ivan
Catholic University of Santa María
Date Issued
19 de marzo de 2026
Type
Article
Volume
41
Issue
3
Series/Report No.
Computational Statistics
ISSN
0943-4062
1613-9658
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.