# Performance of the empirical median for location estimation in heteroscedastic settings

arXiv: https://arxiv.org/abs/2501.16956 · HTML: https://mlsanity.com/paper/2501.16956/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 27 references that are in the map.
- First posted on arXiv 28 Jan 2025.

## Builds on (most cited first, 8 of 8)

- [Mean estimation and regression under heavy-tailed distributions--a survey](https://mlsanity.com/paper/1906.04280/) (2019)
- [Being Robust (in High Dimensions) Can Be Practical](https://mlsanity.com/paper/1703.00893/) (2017)
- [Outlier Robust Mean Estimation with Subgaussian Rates via Stability](https://mlsanity.com/paper/2007.15618/) (2020)
- [Learning Entangled Single-Sample Distributions via Iterative Trimming](https://mlsanity.com/paper/2004.09563/) (2020)
- [Finite-Sample Symmetric Mean Estimation with Fisher Information Rate](https://mlsanity.com/paper/2306.16573/) (2023)
- [Near-Optimal Mean Estimation with Unknown, Heteroskedastic Variances](https://mlsanity.com/paper/2312.02417/) (2023)
- [Non-asymptotic bounds for percentiles of independent non-identical random variables](https://mlsanity.com/paper/1808.07997/) (2018)
- [Estimating location parameters in entangled single-sample distributions](https://mlsanity.com/paper/1907.03087/) (2019)

## Built on by (most cited first, 1 of 1)

- [Algorithms for adaptive and heteroskedastic linear regression at the computational threshold](https://mlsanity.com/paper/2608.18402/) (2026)

## Abstract (arXiv)

We investigate the performance of the empirical median for location estimation in heteroscedastic settings. Specifically, we consider independent symmetric real-valued random variables that share a common but unknown location parameter while having different and unknown scale parameters. Estimation under heteroscedasticity arises naturally in many practical situations and has recently attracted considerable attention. In this work, we analyze the empirical median as an estimator of the common location parameter and derive matching non-asymptotic upper and lower bounds on its estimation error. These results fully characterize the behavior of the empirical median in heteroscedastic settings, clarifying both its robustness and its intrinsic limitations and offering a precise understanding of its performance in modern settings where data quality may vary across sources.