Biometrika· 2026Q1
Rao-Blackwellized e-variables
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- Q1SCImago
- 2026year
Short summary
The expected utility of an e-variable increases when conditioned on a sufficient statistic for any concave utility, mirroring the Rao-Blackwell theorem.
AI-generated from the title and abstract; the full text is not read.
Key points
- Conditioning an e-variable on a sufficient statistic increases its expected utility for concave utilities.
- The result is a generalization of the classic Rao-Blackwell theorem to e-variables.
- A simple proof relies on Jensen's inequality, with more complex proofs also provided.
- Applications include deriving the log-optimal e-variable for linear regression variance testing.
AI-generated from the title and abstract; the full text is not read.
Abstract
Summary We show that for any concave utility, the expected utility of an e-variable can only increase after conditioning on a sufficient statistic, echoing the classic Rao-Blackwell theorem. The simplest form of the result has a straightforward proof using Jensen’s inequality, but we prove more sophisticated versions. We provide several applications of this insight, including a derivation of the log-optimal e-variable for testing the variance in a linear regression model.
The authors' abstract, as published at the source. Biometrika, 2026 · DOI ↗
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Field: Statistics and Probability
Statistics and ProbabilityMathematics