# Do we need to estimate the variance in robust mean estimation?

arXiv: https://arxiv.org/abs/2107.00118 · HTML: https://mlsanity.com/paper/2107.00118/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Jun 2021.

## Built on by (most cited first, 6 of 6)

- [Variance-aware robust reinforcement learning with linear function approximation under heavy-tailed rewards](https://mlsanity.com/paper/2303.05606/) (2023)
- [Non-Asymptotic Guarantees for Robust Statistical Learning under Infinite Variance Assumption](https://mlsanity.com/paper/2201.03182/) (2022)
- [Adaptive Robust Estimator for Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2603.21574/) (2026)
- [Robust variance-regularized risk minimization with concomitant scaling](https://mlsanity.com/paper/2301.11584/) (2023)
- [Breaking the Total Variance Barrier: Sharp Sample Complexity for Linear Heteroscedastic Bandits with Fixed Action Set](https://mlsanity.com/paper/2607.23679/) (2026)
- [STAR-GRPO: Canonical Anchoring and Reliability-First Advantages against Representation-Dependent Reward Hacking](https://mlsanity.com/paper/2609.36900/) (2026)

## Abstract (arXiv)

In this paper, we propose self-tuned robust estimators for estimating the mean of heavy-tailed distributions, which refer to distributions with only finite variances. Our approach introduces a new loss function that considers both the mean parameter and a robustification parameter. By jointly optimizing the empirical loss function with respect to both parameters, the robustification parameter estimator can automatically adapt to the unknown data variance, and thus the self-tuned mean estimator can achieve optimal finite-sample performance. Our method outperforms previous approaches 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. Project source code is available at urlhttps://github.com/statsle/automean.