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

Area of Science:

• Statistics
• Survey Methodology

Background:

• Classical regression estimators in survey sampling are prone to inefficiency and instability due to outliers and model deviations.
• Existing methods struggle to effectively handle contaminated or heterogeneous datasets.

Purpose of the Study:

• To propose a new class of robust regression-type estimators for finite population mean estimation.
• To enhance stability and efficiency in survey sampling, particularly in the presence of outliers and model deviations.

Main Methods:

• Utilized the Generalized M-estimation (GM-estimation) framework for developing new estimators.
• Incorporated adaptive weighting schemes (Mallows-GM, Schweppes-GM, SIS-GM) to mitigate outlier effects.
• Derived analytical expressions for bias and mean square error (MSE) under first-order approximations.

Main Results:

• GM-type estimators demonstrated substantially higher efficiency and robustness compared to OLS and Huber estimators.
• Efficiency gains exceeded 150% in simulations with heavy data contamination.
• Proposed estimators showed strong stability across various tuning parameters and correlation structures.

Conclusions:

• The proposed GM-estimation methodology provides a robust and efficient alternative for mean estimation in survey sampling.
• These estimators are particularly suitable for contaminated and heterogeneous data environments.
• The study advances robust statistical methods for survey data analysis.