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arXiv · 2512.16759

Rao-Blackwellized e-variables

Dante de Roos·Ben Chugg·Peter Grünwald·Aaditya Ramdas
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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.

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Dante de Roos, Ben Chugg, Peter Grünwald, Aaditya Ramdas. 2025-12-18. Rao-Blackwellized e-variables. https://arxiv.org/abs/2512.16759

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