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 arbitrary 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.
SUMMARYWe 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 arbitrary 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. Read More
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