[2107.00118] Self-tuned robust mean estimator

Download PDF of Qiang Sun’s paper titled “Self-Tuned Robust Mean Estimator”

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overview: In this paper, we propose a new self-tuned robust estimator for estimating the mean of distributions with only finite variance. Our method involves introducing a new loss function that considers both the averaging parameter and the robustization parameter. By simultaneously optimizing the empirical loss function with respect to both parameters, the resulting estimator of the robust parameter can automatically adapt to the unknown variance and achieve near-optimal finite-sample performance. Our approach outperforms previous methods in terms of both computational and asymptotic efficiency. Specifically, it does not require cross-validation or Lepski’s method to adjust the robustization parameters, and the variance of the estimator achieves his Cramér-Rao.