The only admissible way of merging arbitrary e-values
Statistics Theory
2025-03-17 v2 Statistics Theory
Abstract
We prove that the only admissible way of merging arbitrary e-values is to use a weighted arithmetic average. This result completes the picture of merging methods for e-values, and generalizes the result of Vovk and Wang (2021, Annals of Statistics, 49(3), 1736--1754) that the only admissible way of symmetrically merging e-values is to use the arithmetic average combined with a constant. Although the proved statement is naturally anticipated, its proof relies on a sophisticated application of optimal transport duality and a minimax theorem.
Cite
@article{arxiv.2409.19888,
title = {The only admissible way of merging arbitrary e-values},
author = {Ruodu Wang},
journal= {arXiv preprint arXiv:2409.19888},
year = {2025}
}