A robust M-estimation framework for spatial autoregressive models: loss function design and optimization strategies

Le résumé fourni par la source

Spatial autoregressive (SAR) models are frequently applied in geographic research to account for spatial dependence. Although robust estimation methods (e.g. M-estimation) within SAR models have been investigated recently, key challenges remain: (1) How should the loss function be rationally designed in M-estimation for SAR models? (2) How can the scale parameter in M-estimation be evaluated? (3) How can the robust optimization problem be solved efficiently? In this research, we derived a closed-form bias-corrected least-squares estimator that outperforms the popular maximum likelihood estimator both numerically and statistically. We replaced the squared Euclidean norm with rational loss functions and then proposed an iteratively re-weighted least-squares scheme to attain a robust solution numerically. Simulation results demonstrate that our robust M-estimators, particularly redescending types, significantly improve estimation accuracy (reducing bias and root-mean-square error) and computational efficiency. In a real-world application with the Boston housing data, our method correctly identifies the underlying 22 outliers and increases the coefficient of determination from 0.78 to 0.90. Our future work will focus on enhancing computational performance through advanced optimization techniques.

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