{"paper":{"title":"The numeraire e-variable and reverse information projection","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ME","stat.TH"],"primary_cat":"math.ST","authors_text":"Aaditya Ramdas, Johannes Ruf, Martin Larsson","submitted_at":"2024-02-29T02:31:42Z","abstract_excerpt":"We consider testing a composite null hypothesis $\\mathcal{P}$ against a point alternative $\\mathsf{Q}$ using e-variables, which are nonnegative random variables $X$ such that $\\mathbb{E}_\\mathsf{P}[X] \\leq 1$ for every $\\mathsf{P} \\in \\mathcal{P}$. This paper establishes a fundamental result: under no conditions whatsoever on $\\mathcal{P}$ or $\\mathsf{Q}$, there exists a special e-variable $X^*$ that we call the numeraire, which is strictly positive and satisfies $\\mathbb{E}_\\mathsf{Q}[X/X^*] \\leq 1$ for every other e-variable $X$. In particular, $X^*$ is log-optimal in the sense that $\\mathbb"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2402.18810","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2402.18810/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}