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

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.