# On the optimality of coin-betting for mean estimation

arXiv: https://arxiv.org/abs/2412.02640 · HTML: https://mlsanity.com/paper/2412.02640/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Dec 2024.

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

- [Confidence Sequences for Generalized Linear Models via Regret Analysis](https://mlsanity.com/paper/2504.16555/) (2025)
- [Testing For Distribution Shifts with Conditional Conformal Test Martingales](https://mlsanity.com/paper/2602.13848/) (2026)
- [STaR-Bets: Sequential Target-Recalculating Bets for Tighter Confidence Intervals](https://mlsanity.com/paper/2505.22422/) (2025)
- [Learning to Bet for Horizon-Aware Anytime-Valid Testing](https://mlsanity.com/paper/2603.19551/) (2026)
- [Statistical Mean Estimation with Coded Relayed Observations](https://mlsanity.com/paper/2505.09098/) (2025)
- [Asymptotically Log-Optimal Bayes-Assisted Confidence Sequences for Bounded Means](https://mlsanity.com/paper/2605.07964/) (2026)
- [Always-On Experimentation](https://mlsanity.com/paper/2609.38695/) (2026)

## Abstract (arXiv)

We consider the problem of testing the mean of a bounded real random variable. We introduce a notion of optimal classes for e-variables and e-processes, and establish the optimality of the coin-betting formulation among e-variable-based algorithmic frameworks for testing and estimating the (conditional) mean. As a consequence, we provide a direct and explicit characterisation of all valid e-variables and e-processes for this testing problem. In the language of classical statistical decision theory, we fully describe the set of all admissible e-variables and e-processes, and identify the corresponding minimal complete class.