# Robust hypothesis testing and distribution estimation in Hellinger distance

arXiv: https://arxiv.org/abs/2011.01848 · HTML: https://mlsanity.com/paper/2011.01848/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Nov 2020.

## Built on by (most cited first, 3 of 3)

- [Communication-constrained hypothesis testing: Optimality, robustness, and reverse data processing inequalities](https://mlsanity.com/paper/2206.02765/) (2022)
- [On Robust Hypothesis Testing with respect to the Hellinger Distance](https://mlsanity.com/paper/2510.16750/) (2025)
- [Density estimation for Hellinger via minimum-distance estimators: mixtures of Gaussians, log-concave, and more](https://mlsanity.com/paper/2606.11469/) (2026)

## Abstract (arXiv)

We propose a simple robust hypothesis test that has the same sample complexity as that of the optimal Neyman-Pearson test up to constants, but robust to distribution perturbations under Hellinger distance. We discuss the applicability of such a robust test for estimating distributions in Hellinger distance. We empirically demonstrate the power of the test on canonical distributions.