A rank-based sequential test of independence

Summary 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 nonsequential 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.