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

翻译：本文提出了新型自调谐鲁棒估计器，用于估计仅具有有限方差的分布均值。我们引入了一种同时考虑均值参数和鲁棒化参数的新损失函数。通过对该经验损失函数关于两个参数进行联合优化，所得鲁棒化参数的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。与现有方法相比，本方法在计算效率与渐近效率方面均表现更优。具体而言，该方法无需通过交叉验证或Lepski方法调节鲁棒化参数，且所提估计器的方差达到了Cramér-Rao下界。