# Anytime-valid sequential testing for elicitable functionals via supermartingales

arXiv: https://arxiv.org/abs/2204.05680 · HTML: https://mlsanity.com/paper/2204.05680/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Apr 2022.

## Built on by (most cited first, 4 of 4)

- [Active, anytime-valid risk controlling prediction sets](https://mlsanity.com/paper/2406.10490/) (2024)
- [A lower confidence sequence for the changing mean of non-negative right heavy-tailed observations with bounded mean](https://mlsanity.com/paper/2210.11133/) (2022)
- [Infinite Action Contextual Bandits with Reusable Data Exhaust](https://mlsanity.com/paper/2302.08551/) (2023)
- [Bet on Features: Anytime-Valid and Feature-Aware Auditing of Conditional Quantile Forecasters](https://mlsanity.com/paper/2607.11653/) (2026)

## Abstract (arXiv)

We design sequential tests for a large class of nonparametric null hypotheses based on elicitable and identifiable functionals. Such functionals are defined in terms of scoring functions and identification functions, which are ideal building blocks for constructing nonnegative supermartingales under the null. This in turn yields sequential tests via Ville's inequality. Using regret bounds from Online Convex Optimization, we obtain rigorous guarantees on the asymptotic power of the tests for a wide range of alternative hypotheses. Our results allow for bounded and unbounded data distributions, assuming that a sub-psi tail bound is satisfied.