{"paper":{"title":"A sharp lower bound for choosing the maximum of an independent sequence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jose A. Islas, Pieter C. Allaart","submitted_at":"2015-11-06T19:56:55Z","abstract_excerpt":"This paper considers a variation of the full-information secretary problem where the random variables to be observed are independent but not necessary identically distributed. The main result is a sharp lower bound for the optimal win probability. Precisely, if $X_1,\\dots,X_n$ are independent random variables with known continuous distributions and $V_n(X_1,\\dots,X_n):=\\sup_\\tau P(X_\\tau=M_n)$, where $M_n:=\\max\\{X_1,\\dots,X_n\\}$ and the supremum is over all stopping times adapted to $X_1,\\dots,X_n$, then $$V_n(X_1,\\dots,X_n)\\geq \\left(1-\\frac{1}{n}\\right)^{n-1},$$ and this bound is attained. T"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.02211","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}