{"ID":2827646,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2512.16759","arxiv_id":"2512.16759","title":"Rao-Blackwellized e-variables","abstract":"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.","short_abstract":"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-varia...","url_abs":"https://arxiv.org/abs/2512.16759","url_pdf":"https://arxiv.org/pdf/2512.16759v1","authors":"[\"Dante de Roos\",\"Ben Chugg\",\"Peter Grünwald\",\"Aaditya Ramdas\"]","published":"2025-12-18T16:56:30Z","proceeding":"math.ST","tasks":"[\"math.ST\",\"math.PR\",\"stat.ME\"]","methods":"[]","has_code":false}