In this paper, we propose new self-tuned robust estimators for estimating the mean of distributions with only finite variances. Our method involves introducing a new loss function that considers both the mean parameter and a robustification parameter. By simultaneously optimizing the empirical loss function with respect to both parameters, the resulting estimator for the robustification parameter can adapt to the unknown variance automatically and can 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 tune the robustification parameter, and the variance of our estimator achieves the Cram\'er-Rao lower bound.

翻译：本文提出了一种新的自调谐稳健估计量，用于估计仅具有有限方差的分布的均值。我们的方法引入了一个新的损失函数，该函数同时考虑了均值参数和稳健化参数。通过同时优化关于这两个参数的经验损失函数，所得的稳健化参数估计量能够自动适应未知方差，并实现接近最优的有限样本性能。我们的方法在计算效率和渐近效率方面均优于以往方法。具体而言，它无需通过交叉验证或Lepski方法对稳健化参数进行调谐，且估计量的方差达到了Cramér-Rao下界。