{"paper":{"title":"A New Look at the Classical Estimation Problem","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.IT","math.IT","stat.TH"],"primary_cat":"math.ST","authors_text":"Paul W. Vos","submitted_at":"2026-07-27T13:52:38Z","abstract_excerpt":"Bahadur's \\emph{Lectures on the Theory of Estimation} develop the classical theory of point estimation inside the geometry of Hilbert space, and they record with unusual honesty where the theory strains: the locally best unbiased estimate depends on the parameter, a two-point parameter space yields an estimate Bahadur calls absurd, the odds ratio in binomial sampling has no unbiased estimate, and the virtues of maximum likelihood enter as heuristics and remain heuristics. We present a subset of the lectures, in Bahadur's notation and development, and at each strain make one small modification:"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.24890","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/2607.24890/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"}