{"paper":{"title":"Universality of e-detectors for ARL control","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","eess.SP","math.IT","stat.ME","stat.TH"],"primary_cat":"math.ST","authors_text":"Aaditya Ramdas","submitted_at":"2026-08-12T23:46:49Z","abstract_excerpt":"An e-detector for a pre-change class $\\mathcal P$ is a nonnegative process $M$ such that $\\mathbb E_P[M_\\tau] \\leq \\mathbb E_P[\\tau]$ for all stopping times $\\tau$ and all $P \\in \\mathcal P$. Thresholding e-detectors controls the average run length (ARL): declaring a change at the first time $T_b$ when $M$ crosses $b$ ensures that $\\inf_{P \\in \\mathcal P}\\mathbb E_P[T] \\geq b$. But e-detectors do substantially more than control the ARL; they also satisfy a \\emph{optional-horizon inequality}: \\[ P(T_b\\leq\\sigma)\\leq \\mathbb E_P[\\sigma]/b \\] for every data-dependent stopping time (monitoring hor"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.12660","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/2608.12660/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"}