English

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}
}
R2 v1 2026-06-28T19:01:34.427Z