# A new and flexible class of sharp asymptotic time-uniform confidence sequences

arXiv: https://arxiv.org/abs/2502.10380 · HTML: https://mlsanity.com/paper/2502.10380/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 25 references that are in the map.
- First posted on arXiv 14 Feb 2025.

## Builds on (most cited first, 5 of 5)

- [Game-theoretic statistics and safe anytime-valid inference](https://mlsanity.com/paper/2210.01948/) (2022)
- [Safe Testing](https://mlsanity.com/paper/1906.07801/) (2019)
- [Time-uniform central limit theory and asymptotic confidence sequences](https://mlsanity.com/paper/2103.06476/) (2021)
- [Near-Optimal Non-Parametric Sequential Tests and Confidence Sequences with Possibly Dependent Observations](https://mlsanity.com/paper/2212.14411/) (2022)
- [Power of Ordered Hypothesis Testing](https://mlsanity.com/paper/1606.01969/) (2016)

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

- [seMCD: Sequentially implemented Monte Carlo depth computation with statistical guarantees](https://mlsanity.com/paper/2507.06227/) (2025)

## Abstract (arXiv)

Confidence sequences are anytime-valid analogues of classical confidence intervals that do not suffer from multiplicity issues under optional continuation of the data collection. As in classical statistics, asymptotic confidence sequences are a nonparametric tool showing under which high-level assumptions asymptotic coverage is achieved so that they also give a certain robustness guarantee against distributional deviations. In this paper, we propose a new flexible class of confidence sequences yielding sharp asymptotic time-uniform confidence sequences under mild assumptions. Furthermore, we highlight the connection to corresponding sequential testing problems and detail the underlying limit theorem.