2025/12/18 by de Roos, Dante, Chugg, Ben, Grünwald, Peter +1
#FOS: Computer and information sciences #FOS: Mathematics #Methodology (stat.ME) #Probability (math.PR) #Statistics Theory (math.ST)
paper · doi:10.48550/arxiv.2512.16759
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.