Improved thresholds for e-values
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866912624231317504 |
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| author | Blier-Wong, Christopher Wang, Ruodu |
| author_facet | Blier-Wong, Christopher Wang, Ruodu |
| contents | The rejection threshold used for e-values and e-processes is by default set to $1/α$ for a guaranteed type-I error control at $α$, based on Markov's and Ville's inequalities. This threshold can be wasteful in practical applications. We discuss how this threshold can be improved under additional distributional assumptions on the e-values; some of these assumptions are naturally plausible and empirically observable, without knowing explicitly the form or model of the e-values. For small values of $α$, the threshold can roughly be improved (divided) by a factor of $2$ for decreasing or unimodal densities, and by a factor of $e$ for decreasing or unimodal-symmetric densities of log-transformed e-values. Moreover, we propose to use the supremum of comonotonic e-values, which is shown to preserve the type-I error guarantee. We also propose some preliminary methods to boost e-values in the e-BH procedure under some distributional assumptions while controlling the false discovery rate. Through a series of simulation studies, we demonstrate the effectiveness of our proposed methods in various testing scenarios, showing enhanced power. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2408_11307 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Improved thresholds for e-values Blier-Wong, Christopher Wang, Ruodu Statistics Theory 62G10, 62F03, 60E15 The rejection threshold used for e-values and e-processes is by default set to $1/α$ for a guaranteed type-I error control at $α$, based on Markov's and Ville's inequalities. This threshold can be wasteful in practical applications. We discuss how this threshold can be improved under additional distributional assumptions on the e-values; some of these assumptions are naturally plausible and empirically observable, without knowing explicitly the form or model of the e-values. For small values of $α$, the threshold can roughly be improved (divided) by a factor of $2$ for decreasing or unimodal densities, and by a factor of $e$ for decreasing or unimodal-symmetric densities of log-transformed e-values. Moreover, we propose to use the supremum of comonotonic e-values, which is shown to preserve the type-I error guarantee. We also propose some preliminary methods to boost e-values in the e-BH procedure under some distributional assumptions while controlling the false discovery rate. Through a series of simulation studies, we demonstrate the effectiveness of our proposed methods in various testing scenarios, showing enhanced power. |
| title | Improved thresholds for e-values |
| topic | Statistics Theory 62G10, 62F03, 60E15 |
| url | https://arxiv.org/abs/2408.11307 |