Robust and Machine Learning Augmented Estimation of Finite-Population Variance using Auxiliary Information under Measurement Error and Complex Survey Designs

Abstract

Accurate finite-population variance estimation is essential for survey inference but is compromised by measurement error, outliers, and complex designs. This paper proposes a unified framework integrating measurement-error correction, robust statistics, and machine learning (ML) for variance estimation using auxiliary information. We develop corrected ratio, regression, and exponential-type estimators adjusted for additive errors, enhanced with bounded-influence M-estimation and Huber-loss-trained ML algorithms (Gradient-Boosted Machines and Random Forests) to capture non-linear auxiliary relationships Extensive Monte Carlo simulations and empirical applications using the Agricultural Resource Management Survey (ARMS) and Current Population Survey (CPS) data quantify the framework's superiority. Results demonstrate that while measurement error inflates naive variance estimates by approximately the error variance (σ_e^2), our corrected auxiliary-based estimators reduce mean squared error (MSE) by 60–80%. The integration of ML captures non-linearities, yielding an additional 20–40% MSE reduction over linear methods. Crucially, under 20% data contamination, standard ML estimators degrade rapidly, whereas the proposed robust GBM-Huber estimator exhibits graceful degradation, maintaining MSE reductions of up to 95% relative to the naive Horvitz–Thompson estimator. In empirical applications, the robust ML estimator achieves Relative Efficiencies (RE) of 1742% and 2676% compared to naive estimators. Furthermore, the methodology seamlessly adapts to complex designs, with stratified Neyman allocation maximizing efficiency, and maintains highly feasible computation times (0.5 seconds). Ultimately, this robust, ML-augmented approach provides a highly efficient, outlier-resistant, and computationally practical solution for modern survey variance estimation.