The Median-of-Means Estimator under Adversarial Contamination

X. de Juan Soriano, S. Mazuelas

The Median-of-Means (MoM) estimator, widely recognized for its (minimax) optimality in the i.i.d. setting, lacks a comprehensive characterization in the presence of adversarial contamination. This work establishes error bounds for MoM under such contamination across various distribution classes. In particular, we prove that MoM is (minimax) optimal in the class of distributions with finite variance, and in the class of distributions with finite absolute $(1+r)$-th moment. Notably, we show that MoM is particularly suited for symmetric distributions, but it is sub-optimal for light-tailed distributions. Overall, the theoretical results presented provide a comprehensive characterization of the capabilities of the MoM estimator under adversarial contamination.

Keywords: mean estimation, median of means, adversarial contamination, robust estimation, minimax bounds, minimax optimality, robustness, mom, concentration inequalities

Non Parametric Statistics II
June 12, 2025  7:00 PM
Auditorio 1. Ricard Vinyes

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