Rao-Blackwellized e-variables
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866917154495922176 |
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| author | de Roos, Dante Chugg, Ben Grünwald, Peter Ramdas, Aaditya |
| author_facet | de Roos, Dante Chugg, Ben Grünwald, Peter Ramdas, Aaditya |
| contents | We show that for any concave utility, the expected utility of an e-variable can only increase after conditioning on a sufficient statistic. The simplest form of the result has an extremely straightforward proof, which follows from a single application of Jensen's inequality. Similar statements hold for compound e-variables, asymptotic e-variables, and e-processes. These results echo the Rao-Blackwell theorem, which states that the expected squared error of an estimator can only decrease after conditioning on a sufficient statistic. We provide several applications of this insight, including a simplified derivation of the log-optimal e-variable for linear regression with known variance. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_16759 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Rao-Blackwellized e-variables de Roos, Dante Chugg, Ben Grünwald, Peter Ramdas, Aaditya Statistics Theory Probability Methodology We show that for any concave utility, the expected utility of an e-variable can only increase after conditioning on a sufficient statistic. The simplest form of the result has an extremely straightforward proof, which follows from a single application of Jensen's inequality. Similar statements hold for compound e-variables, asymptotic e-variables, and e-processes. These results echo the Rao-Blackwell theorem, which states that the expected squared error of an estimator can only decrease after conditioning on a sufficient statistic. We provide several applications of this insight, including a simplified derivation of the log-optimal e-variable for linear regression with known variance. |
| title | Rao-Blackwellized e-variables |
| topic | Statistics Theory Probability Methodology |
| url | https://arxiv.org/abs/2512.16759 |