Robust Finite Population Mean Estimation under Outlier Contamination Using Adaptive UK’s Redescending M-Estimation

Abstract

The efficient estimation of population parameters under non-ideal data conditions remains a critical challenge in survey sampling. Traditional estimators based on ordinary least squares (OLS) often yield unreliable results when datasets contain outliers or deviate from normality. This study introduces a new class of ratio-type estimators that incorporate population parameters such as the median and decile mean and are developed under both OLS and UK’s redescending M-estimation frameworks. To further enhance robustness, an adaptive variant of the UK’s redescending M-estimator is proposed, which automatically adjusts its tuning constant based on the degree of contamination. Analytical derivations of bias and mean square error (MSE) confirm the superiority of the proposed estimators over their OLS counterparts. Empirical validation using realworld socio-economic survey data and extensive simulation studies across varying sample sizes, outlier rates, and distributional forms demonstrate that the adaptive UK’s redescending estimator achieves substantial efficiency gains and reduced bias, even under high contamination levels. The results establish the adaptive redescending M-estimation approach as a robust and computationally efficient alternative for finite population mean estimation in the presence of outliers.OPEN ACCESS Received: 10/10/2025 Accepted: 03/11/2025 Published: 23/01/2026

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