# A Rank-Based Sequential Test of Independence

arXiv: https://arxiv.org/abs/2305.13818 · HTML: https://mlsanity.com/paper/2305.13818/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 May 2023.

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

- [Combining Evidence Across Filtrations](https://mlsanity.com/paper/2402.09698/) (2024)
- [Optimal Anytime-Valid Tests for Composite Nulls](https://mlsanity.com/paper/2512.20039/) (2025)
- [A complete characterization of sequential testability and change detectability in i.i.d. models](https://mlsanity.com/paper/2609.05752/) (2026)

## Abstract (arXiv)

We consider the problem of independence testing for two univariate random variables in a sequential setting. By leveraging recent developments on safe, anytime-valid inference, we propose a test with time-uniform type I error control and derive explicit bounds on the finite sample performance of the test. We demonstrate the empirical performance of the procedure in comparison to existing sequential and non-sequential independence tests. Furthermore, since the proposed test is distribution free under the null hypothesis, we empirically simulate the gap due to Ville's inequality, the supermartingale analogue of Markov's inequality, that is commonly applied to control type I error in anytime-valid inference, and apply this to construct a truncated sequential test.