Defines empirical sensitivity and proves Ω(η + √(η d/n)) lower bound (tight up to logs) for any Gaussian mean estimator achieving optimal O(√(d/n)) ℓ₂ error.
Proceedings of the 32nd International Conference on Algorithmic Learning Theory , series =
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Robust Statistical Estimators with Bounded Empirical Sensitivity
Defines empirical sensitivity and proves Ω(η + √(η d/n)) lower bound (tight up to logs) for any Gaussian mean estimator achieving optimal O(√(d/n)) ℓ₂ error.