# Median Regularity and Honest Inference

arXiv: https://arxiv.org/abs/2206.02954 · HTML: https://mlsanity.com/paper/2206.02954/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Jun 2022.

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

- [On the Precise Asymptotics of Universal Inference](https://mlsanity.com/paper/2503.14717/) (2025)

## Abstract (arXiv)

We introduce a new notion of regularity of an estimator called median regularity. We prove that uniformly valid (honest) inference for a functional is possible if and only if there exists a median regular estimator of that functional. To our knowledge, such a notion of regularity that is necessary for uniformly valid inference is unavailable in the literature.