arXiv:2605.27718v1 Announce Type: cross 
Abstract: Moment-based estimation is a theoretically attractive approach to parametric inference, especially when likelihood-based estimation is unavailable, misspecified, or computationally inconvenient. However, the moment equations involve sample averages, which makes moment-based estimation sensitive to outliers. We propose the SGR-GMM algorithm, a robust generalized method of moments (GMM) procedure that uses a spectral gradient reweighting (SGR) primitive to soft-reweight the per-observation gradients during the moment-matching optimization. Our analysis has three layers. First, for a fixed center, the SGR primitive is formulated as an entropy-regularized spectral game between a sample-weight player and a density-matrix player, which is analyzed using classical multiplicative-weights and matrix-multiplicative-weights regret bounds. Second, we establish explicit convergence radius and finite termination bound for the fixed-center updates in the SGR primitive. Third, we prove a local finite-sample parameter estimation error bound with explicit dependence on the contamination fraction, inlier gradient stability, local GMM identification strength, and optimization accuracy. We further specialize the SGR-GMM algorithm to obtain a robust diagonally-weighted GMM (DGMM) estimator for estimating heteroscedastic low-rank Gaussian mixtures observed under additive Gaussian noise and strong contamination. In the numerical experiments, the SGR primitive produces nearly-oracle gradient estimation and the robust DGMM specialization substantially improves over non-robust moment baselines. The code and data are available at https://github.com/liu-lzhang/sgr-gmm.

تم اقتراح خوارزمية جديدة تُدعى SGR-GMM للتقدير القائم على اللحظات بشكل قوي، والتي تعالج حساسية الطرق التقليدية المعتمدة على اللحظات تجاه القيم الشاذة. تستخدم هذه الطريقة إعادة وزن التدرجات الطيفية لتحسين مطابقة اللحظات، مما يعزز موثوقية الاستدلال البارامتري عندما لا تكون التقديرات المعتمدة على الاحتمالية ممكنة.

Se ha propuesto un nuevo algoritmo llamado SGR-GMM para la estimación robusta basada en momentos, que aborda la sensibilidad de los métodos tradicionales basados en momentos a los valores atípicos. Este enfoque utiliza el reponderado de gradientes espectrales para optimizar la coincidencia de momentos, mejorando la fiabilidad de la inferencia paramétrica cuando la estimación basada en la verosimilitud no es factible.

Un nouvel algorithme nommé SGR-GMM a été proposé pour une estimation robuste basée sur les moments, qui traite la sensibilité des méthodes traditionnelles basées sur les moments aux valeurs aberrantes. Cette approche utilise le réajustement spectral des gradients pour optimiser l'appariement des moments, améliorant ainsi la fiabilité de l'inférence paramétrique lorsque l'estimation basée sur la vraisemblance n'est pas faisable.

A new algorithm named SGR-GMM has been proposed for robust moment-based estimation, which addresses the sensitivity of traditional moment-based methods to outliers. This approach utilizes spectral gradient reweighting to optimize moment-matching, enhancing the reliability of parametric inference when likelihood-based estimation is not feasible.