Fast Approximate MM-Estimation for Outlier Robust Model Selection

2026-06-25

AI Summary

This study addresses the high computational cost of iterative robust estimators in the presence of multiple candidate models by proposing the FAMM method, which for the first time efficiently approximates MM-estimators in a weighted least squares form. By leveraging weights derived from a full-data MM-estimate to construct a weighted least squares approximation, FAMM substantially reduces computational burden while preserving model selection consistency. The approach integrates MM estimation, weighted least squares fitting, bootstrap resampling, and robust inference techniques. Extensive simulations and an empirical analysis of NBA data demonstrate that FAMM achieves high computational efficiency without compromising model selection accuracy, effectively balancing statistical performance and computational tractability.

Abstract

Stratified robust model selection reduces the impact of large residuals and overrepresented outliers in bootstrap samples but is computationally intensive when fitting iteratively-solved robust estimators across many candidate models. We propose FAMM, a Fast Approximate MM-estimator, implemented as a weighted least squares fit with weights derived from a full-data MM-estimator, to reduce this computational cost. Using extensive artificial simulations and applications to National Basketball Association data, we show that substituting the MM-estimator with FAMM preserves model selection performance while achieving a substantial computational speedup. Furthermore, we demonstrate that FAMM satisfies the required conditions for model selection consistency.

Problem

• robust model selection
• MM-estimation
• computational cost
• outlier
• bootstrap

Innovation

• Fast Approximate MM-estimation
• Robust Model Selection
• Weighted Least Squares
• Computational Efficiency
• Model Selection Consistency