# Efficient median of means estimator

arXiv: https://arxiv.org/abs/2305.18681 · HTML: https://mlsanity.com/paper/2305.18681/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 1 of its 14 references that are in the map.
- First posted on arXiv 30 May 2023.

## Builds on (most cited first, 1 of 1)

- [Mean estimation and regression under heavy-tailed distributions--a survey](https://mlsanity.com/paper/1906.04280/) (2019)

## Built on by (most cited first, 7 of 7)

- [Order-Optimal Sequential 1-Bit Mean Estimation in General Tail Regimes](https://mlsanity.com/paper/2604.07796/) (2026)
- [Sequential 1-bit Mean Estimation with Near-Optimal Sample Complexity](https://mlsanity.com/paper/2509.21940/) (2025)
- [Multiple-policy Evaluation via Density Estimation](https://mlsanity.com/paper/2404.00195/) (2024)
- [Open Problem: Is Interaction Necessary for Order-Optimal 1-bit Mean Estimation?](https://mlsanity.com/paper/2607.02896/) (2026)
- [Classical Shadows with Improved Median-of-Means Estimation](https://mlsanity.com/paper/2412.03381/) (2024)
- [On the Optimality of the Median-of-Means Estimator under Adversarial Contamination](https://mlsanity.com/paper/2510.07867/) (2025)
- [Median-of-Means as an Extremal Convex Estimator and a Nonconvex Route to the Trimmed Oracle](https://mlsanity.com/paper/2609.01689/) (2026)

## Abstract (arXiv)

The goal of this note is to present a modification of the popular median of means estimator that achieves sub-Gaussian deviation bounds with nearly optimal constants under minimal assumptions on the underlying distribution. We build on a recent work on the topic by the author, and prove that desired guarantees can be attained under weaker requirements.