Robust regression-based logarithmic estimators for efficient mean estimation in ranked set sampling

Abstract

Accurate estimation of the population mean becomes challenging in the presence of outliers, especially when conventional estimators are implemented under simple random sampling. Ranked set sampling, known for its efficiency gains through judgment-based ranking, further suffers when extreme observations distort the estimation process. To address these issues, this study proposes a new class of robust regression-based logarithmic estimators for efficient population mean estimation under Ranked set sampling. The proposed estimators integrate robust regression techniques such as Huber-M, Huber-MM, least trimmed squares, least median of squares, Hampel-M, and Tukey-M with a logarithmic adjustment structure to minimize the impact of outliers while using auxiliary information. Theoretical properties such as bias and mean square error are derived under Ranked set sampling. Analytical efficiency comparisons demonstrate that the proposed class consistently achieves lower Mean sqaure error than several adapted families of robust estimators under Ranked set sampling. The theoretical results are validated with an extensive simulation study based on artificially generated symmetric and asymmetric populations and a real-data application with intentionally contaminated datasets, further validates the superiority of the proposed estimators.

Keywords

• Mean square error
• outliers
• ranked set sampling
• robust regression

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