Efficient pseudo Rao-Blackwellized estimator in ranked sampling

Document Type : Original Article

Authors

Bardia Panahbehagh ¹

Mahdi Salehi ²

¹ Department of Mathematics‎, ‎Faculty of Mathematics and Computer Science‎, ‎Kharazmi University‎, ‎Tehran‎, ‎Iran

² Department of Mathematics and Statistics‎, ‎University of Neyshabur‎, ‎Neyshabur‎, ‎Iran

10.22067/smps.2026.99259.1061

Abstract

‎Ranked set sampling (RSS) and judgment post-stratification (JPS) are efficient sampling designs that rely on ranking units without requiring full measurement, typically through visual inspection or the use of auxiliary information. In their standard forms, including multi-ranker RSS, only a portion of the available ranking information is utilized, and the corresponding Rao–Blackwellized estimators are generally unavailable in closed form. In this paper, we propose two practical pseudo Rao–Blackwellization approaches that enhance RSS and JPS by incorporating ranking information from all selected sets. The resulting estimators admit closed-form expressions, make more complete use of the available ranking information for each measured unit, and mitigate the impact of inaccurate rankings from individual sets. We further extend the proposed framework to other ranked sampling designs, including median RSS and extreme RSS, and investigate the performance of the resulting estimators under both symmetric and asymmetric populations. Finally, we analyze two real data sets to illustrate the practical applicability of the proposed methods and to corroborate the findings from the simulation studies.

Keywords

Efficiency

‎Judgment

‎Median ranked set sampling

‎Post-stratification

‎Ranked set sampling

‎Rao-Blackwellization

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