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<p>Classical regression type estimators in survey sampling often suffer from inefficiency and instability in the presence of outliers and model deviations. To address these issues, this study proposes a a new class of regression-type estimators for finite population mean using Generalized M-estimation (GM-estimation) framework within both simple random sampling without replacement (SRSWOR) and stratified double sampling designs. The proposed Mallows-GM, Schweppes-GM and SIS-GM estimators incorporate adaptive weighting schemes that jointly mitigate the effect of vertical outliers and high-leverage points. Analytical expressions for bias and mean square error (MSE) are derived under first-order approximations. Extensive Monte Carlo simulations and sensitivity analysis demonstrate that GM-type estimators achieve substantially higher efficiency and robustness than both ordinary least squares and Huber-based counterparts, with efficiency gains exceeding 150% under heavy contamination. The estimators also exhibit strong stability across varying tuning parameters and correlation structures. Overall, the proposed methodology offers a robust and efficient alternative for mean estimation in survey sampling, particularly suitable for contaminated and heterogeneous data environments.</p>

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A robust methodology for finite population mean estimation based on Generalized M estimation

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  • 出版模式：

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  • 发表日期：

    2026年1月13日

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  • Khaled Ali Abuhasel

摘要

Classical regression type estimators in survey sampling often suffer from inefficiency and instability in the presence of outliers and model deviations. To address these issues, this study proposes a a new class of regression-type estimators for finite population mean using Generalized M-estimation (GM-estimation) framework within both simple random sampling without replacement (SRSWOR) and stratified double sampling designs. The proposed Mallows-GM, Schweppes-GM and SIS-GM estimators incorporate adaptive weighting schemes that jointly mitigate the effect of vertical outliers and high-leverage points. Analytical expressions for bias and mean square error (MSE) are derived under first-order approximations. Extensive Monte Carlo simulations and sensitivity analysis demonstrate that GM-type estimators achieve substantially higher efficiency and robustness than both ordinary least squares and Huber-based counterparts, with efficiency gains exceeding 150% under heavy contamination. The estimators also exhibit strong stability across varying tuning parameters and correlation structures. Overall, the proposed methodology offers a robust and efficient alternative for mean estimation in survey sampling, particularly suitable for contaminated and heterogeneous data environments.