2026-03-01
Supermartingales for one-sided tests: Sufficient monotone likelihood ratios are sufficient
Publication
Publication
Statistics and Probability Letters , Volume 229 p. 110574:1- 110574:5
The t-statistic is a widely-used scale-invariant statistic for testing the null hypothesis that the mean is zero. Martingale methods enable sequential testing with the t-statistic at every sample size, while controlling the probability of falsely rejecting the null. For one-sided sequential tests, which reject when the t-statistic is too positive, a natural question is whether they also control false rejection when the true mean is negative. We prove that this is the case using monotone likelihood ratios and sufficient statistics. We develop applications to the scale-invariant t-test, the location-invariant χ 2 -test and sequential linear regression with nuisance covariates.
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| , , , , | |
| doi.org/10.1016/j.spl.2025.110574 | |
| Statistics and Probability Letters | |
| Flexible Statistical Inference | |
| Organisation | Centrum Wiskunde & Informatica, Amsterdam (CWI), The Netherlands |
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Grünwald, P., & Koolen-Wijkstra, W. (2026). Supermartingales for one-sided tests: Sufficient monotone likelihood ratios are sufficient. Statistics and Probability Letters, 229, 110574:1–110574:5. doi:10.1016/j.spl.2025.110574 |
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