A Rank-Based Sequential Test of Independence
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Date
2024-12
Publication Type
Journal Article
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yes
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Abstract
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.
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published
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Journal / series
Volume
111 (4)
Pages / Article No.
1169 - 1186
Publisher
Oxford University Press
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Edition / version
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Software
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Date collected
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Subject
Independence; Sequential test; Sequential ranks; Test Martingale; E-value
Organisational unit
02537 - Seminar für Statistik (SfS) / Seminar for Statistics (SfS)