{"paper":{"title":"Beyond Modern Asymptotics for Log-Likelihood Ratios in Logistic Regression","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.IT","cs.LG","math.IT","stat.TH"],"primary_cat":"math.ST","authors_text":"Hugo Chardon, Nikita Zhivotovskiy, Reese Pathak","submitted_at":"2026-08-03T17:07:41Z","abstract_excerpt":"We characterize the finite sample behavior of the log-likelihood ratio statistic in binary logistic regression, uniformly over both the design and the target parameter. For $n\\geq d\\geq 3$, we determine, up to universal constants, its worst case $(1-\\delta)$ quantile over all fixed collections of design vectors and all target parameters: \\[ d\\log\\left(\\frac{e n}{d}\\right)+\\log\\left(\\frac{1}{\\delta}\\right). \\] This is a nonasymptotic analogue of the Wilks $\\chi^2_d$ phenomenon and requires no regularity assumptions on the design. The low dimensional cases exhibit unusual behavior. The worst cas"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.02507","kind":"arxiv","version":1},"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/2608.02507/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"}