{"ID":2830749,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2512.09708","arxiv_id":"2512.09708","title":"A simple geometric proof for the characterisation of e-merging functions","abstract":"E-values offer a powerful framework for aggregating evidence across different (possibly dependent) statistical experiments. A fundamental question is to identify e-merging functions, namely mappings that merge several e-values into a single valid e-value. A simple and elegant characterisation of this function class was recently obtained by Wang(2025), though via technically involved arguments. This note gives a short and intuitive geometric proof of the same characterisation, based on a supporting hyperplane argument applied to concave envelopes. We also show that the result holds even without imposing monotonicity in the definition of e-merging functions, which was needed for the existing proof. This shows that any non-monotone merging rule is automatically dominated by a monotone one, and hence extending the definition beyond the monotone case brings no additional generality.","short_abstract":"E-values offer a powerful framework for aggregating evidence across different (possibly dependent) statistical experiments. A fundamental question is to identify e-merging functions, namely mappings that merge several e-values into a single valid e-value. A simple and elegant characterisation of this function class was...","url_abs":"https://arxiv.org/abs/2512.09708","url_pdf":"https://arxiv.org/pdf/2512.09708v3","authors":"[\"Eugenio Clerico\"]","published":"2025-12-10T14:53:37Z","proceeding":"math.ST","tasks":"[\"math.ST\"]","methods":"[\"Generative Adversarial Network\"]","has_code":false}