# Rao-Blackwellized e-variables

arXiv: https://arxiv.org/abs/2512.16759 · HTML: https://mlsanity.com/paper/2512.16759/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Dec 2025.

## Built on by (most cited first, 3 of 3)

- [Bentkus-type asymptotic e-values](https://mlsanity.com/paper/2606.06332/) (2026)
- [Efficient Online LLM Watermark Detection via Rao-Blackwellized E-Processes](https://mlsanity.com/paper/2607.21958/) (2026)
- [Sequential Conditional Independence Testing with Machine Learning Models](https://mlsanity.com/paper/2610.11388/) (2026)

## Abstract (arXiv)

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.