# Sub-Gaussian estimators of the mean of a random vector

arXiv: https://arxiv.org/abs/1702.00482 · HTML: https://mlsanity.com/paper/1702.00482/

## Key facts

- Cited by 47 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Feb 2017.

## Built on by (most cited first, 30 of 47)

- [Robust and Differentially Private Mean Estimation](https://mlsanity.com/paper/2102.09159/) (2021)
- [Efficient Mean Estimation with Pure Differential Privacy via a Sum-of-Squares Exponential Mechanism](https://mlsanity.com/paper/2111.12981/) (2021)
- [Covariance-Aware Private Mean Estimation Without Private Covariance Estimation](https://mlsanity.com/paper/2106.13329/) (2021)
- [Byzantine-Robust Federated Learning with Optimal Statistical Rates and Privacy Guarantees](https://mlsanity.com/paper/2205.11765/) (2022)
- [Privacy Induces Robustness: Information-Computation Gaps and Sparse Mean Estimation](https://mlsanity.com/paper/2211.00724/) (2022)
- [Mirror Descent Strikes Again: Optimal Stochastic Convex Optimization under Infinite Noise Variance](https://mlsanity.com/paper/2202.11632/) (2022)
- [A New Approach to Learning Linear Dynamical Systems](https://mlsanity.com/paper/2301.09519/) (2023)
- [Distribution-Free Robust Linear Regression](https://mlsanity.com/paper/2102.12919/) (2021)
- [Rethinking Backdoor Attacks](https://mlsanity.com/paper/2307.10163/) (2023)
- [Outlier-Robust Sparse Mean Estimation for Heavy-Tailed Distributions](https://mlsanity.com/paper/2211.16333/) (2022)
- [High-probability minimax lower bounds](https://mlsanity.com/paper/2406.13447/) (2024)
- [On the benefits of maximum likelihood estimation for Regression and Forecasting](https://mlsanity.com/paper/2106.10370/) (2021)
- [Provable Benefit of Mixup for Finding Optimal Decision Boundaries](https://mlsanity.com/paper/2306.00267/) (2023)
- [Time-Uniform Confidence Spheres for Means of Random Vectors](https://mlsanity.com/paper/2311.08168/) (2023)
- [Order-Optimal Sequential 1-Bit Mean Estimation in General Tail Regimes](https://mlsanity.com/paper/2604.07796/) (2026)
- [Robust Methods for High-Dimensional Linear Learning](https://mlsanity.com/paper/2208.05447/) (2022)
- [High-dimensional Location Estimation via Norm Concentration for Subgamma Vectors](https://mlsanity.com/paper/2302.02497/) (2023)
- [Finite-Sample Symmetric Mean Estimation with Fisher Information Rate](https://mlsanity.com/paper/2306.16573/) (2023)
- [Sequential 1-bit Mean Estimation with Near-Optimal Sample Complexity](https://mlsanity.com/paper/2509.21940/) (2025)
- [Robust Online Convex Optimization in the Presence of Outliers](https://mlsanity.com/paper/2107.01881/) (2021)
- [A survey on secure decentralized optimization and learning](https://mlsanity.com/paper/2408.08628/) (2024)
- [Improved Regret Bounds for Linear Bandits with Heavy-Tailed Rewards](https://mlsanity.com/paper/2506.04775/) (2025)
- [Robust supervised learning with coordinate gradient descent](https://mlsanity.com/paper/2201.13372/) (2022)
- [On Medians of (Randomized) Pairwise Means](https://mlsanity.com/paper/2211.00603/) (2022)
- [Robust Stochastic Optimization via Gradient Quantile Clipping](https://mlsanity.com/paper/2309.17316/) (2023)
- [Minimax Linear Regression under the Quantile Risk](https://mlsanity.com/paper/2406.12145/) (2024)
- [Locally minimax optimal confidence sets for the best model](https://mlsanity.com/paper/2503.21639/) (2025)
- [Regularized least squares learning with heavy-tailed noise is minimax optimal](https://mlsanity.com/paper/2505.14214/) (2025)
- [The Empirical Mean is Minimax Optimal for Local Glivenko-Cantelli](https://mlsanity.com/paper/2410.02835/) (2024)
- [Robust Gradient Descent for Phase Retrieval](https://mlsanity.com/paper/2410.10623/) (2024)

## Abstract (arXiv)

We study the problem of estimating the mean of a random vector X given a sample of N independent, identically distributed points. We introduce a new estimator that achieves a purely sub-Gaussian performance under the only condition that the second moment of X exists. The estimator is based on a novel concept of a multivariate median.