E-values and sequential power-one tests for monotonicity and unimodality
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| Format: | Preprint |
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2026
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| _version_ | 1866913055228559360 |
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| author | Wang, Hongjian Ramdas, Aaditya |
| author_facet | Wang, Hongjian Ramdas, Aaditya |
| contents | We develop e-values and e-processes testing the null hypothesis that a distribution over nonnegative integers is monotone, and that a distribution over integers is unimodal given a certain mode. Our e-processes lead to tests of power one under any non-null distribution with a sequence of i.i.d. observations, and consistent set-valued mode estimators that eventually equal the true set of modes. Additionally, we characterize the set of all e-values, and therefore the set of all valid tests, with one monotone and unimodal observation, as well as the most powerful e-value for a fixed alternative. We then show that many of our results can be generalized to continuous random variables, relating them to the existing results in the shape-constrained inference literature. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_20612 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | E-values and sequential power-one tests for monotonicity and unimodality Wang, Hongjian Ramdas, Aaditya Statistics Theory Probability We develop e-values and e-processes testing the null hypothesis that a distribution over nonnegative integers is monotone, and that a distribution over integers is unimodal given a certain mode. Our e-processes lead to tests of power one under any non-null distribution with a sequence of i.i.d. observations, and consistent set-valued mode estimators that eventually equal the true set of modes. Additionally, we characterize the set of all e-values, and therefore the set of all valid tests, with one monotone and unimodal observation, as well as the most powerful e-value for a fixed alternative. We then show that many of our results can be generalized to continuous random variables, relating them to the existing results in the shape-constrained inference literature. |
| title | E-values and sequential power-one tests for monotonicity and unimodality |
| topic | Statistics Theory Probability |
| url | https://arxiv.org/abs/2604.20612 |