{"paper":{"title":"Asymptotic optimality theory of confidence intervals of the mean","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Achal Bassamboo, Sandeep Juneja, Vikas Deep","submitted_at":"2025-01-31T13:31:43Z","abstract_excerpt":"We address the classical problem of constructing confidence intervals (CIs) for the mean of a distribution, given \\(N\\) i.i.d. samples, such that the CI contains the true mean with probability at least \\(1 - \\delta\\), where \\(\\delta \\in (0,1)\\). We characterize three distinct learning regimes based on the minimum achievable limiting width of any CI as the sample size \\(N_{\\delta} \\to \\infty\\) and \\(\\delta \\to 0\\). In the first regime, where \\(N_{\\delta}\\) grows slower than \\(\\log(1/\\delta)\\), the limiting width of any CI equals the width of the distribution's support, precluding meaningful inf"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.19126","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/2501.19126/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"}