English

Optimized combination of independent or simultaneous e-values

Methodology 2026-03-12 v1 Probability

Abstract

We show that a class of optimized e-value combinations, arising from a standard construction of e-processes, remains valid even when the tuning parameter is optimized based on the data. This result holds for independent e-values, and, more generally, for a new class called simultaneous e-variables, whose dependence structure lies between independence and sequential validity. We further propose an improved combination test for such e-values based on elementary symmetric polynomials.

Cite

@article{arxiv.2603.10329,
  title  = {Optimized combination of independent or simultaneous e-values},
  author = {Jiahao Ming and Yi Shen and Ruodu Wang},
  journal= {arXiv preprint arXiv:2603.10329},
  year   = {2026}
}
R2 v1 2026-07-01T11:14:01.251Z