The only admissible way of merging arbitrary e-values

Ruodu Wang

The only admissible way of merging arbitrary e-values

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arxiv 2409.19888 v2 pith:JVAQ3Z32 submitted 2024-09-30 math.ST stat.TH

Ruodu Wang This is my paper · ORCID

classification math.STstat.TH

keywords e-valuesmergingadmissibleonlyarbitraryarithmeticaverageresult

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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.

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