{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:XO6X6HQTDFS56ORNFR664OMMDY","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"6dca3a4ec54c859886fd3b2e3c1a966cc33adaa18606ba4a3c2a422aa41fb056","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2013-09-16T16:38:20Z","title_canon_sha256":"998be5c6268602c6ddb0855ae67994b70a97ffe7dd3cd8a7c48218e171aa1237"},"schema_version":"1.0","source":{"id":"1309.4029","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.4029","created_at":"2026-05-18T01:36:21Z"},{"alias_kind":"arxiv_version","alias_value":"1309.4029v2","created_at":"2026-05-18T01:36:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.4029","created_at":"2026-05-18T01:36:21Z"},{"alias_kind":"pith_short_12","alias_value":"XO6X6HQTDFS5","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"XO6X6HQTDFS56ORN","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"XO6X6HQT","created_at":"2026-05-18T12:28:06Z"}],"graph_snapshots":[{"event_id":"sha256:d236106aa1c8b5006e025749fb7e73e3314edf34f3a5f71a32c31cbdc743cb02","target":"graph","created_at":"2026-05-18T01:36:21Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Concentration inequalities quantify the deviation of a random variable from a fixed value. In spite of numerous applications, such as opinion surveys or ecological counting procedures, few concentration results are known for the setting of sampling without replacement from a finite population. Until now, the best general concentration inequality has been a Hoeffding inequality due to Serfling [Ann. Statist. 2 (1974) 39-48]. In this paper, we first improve on the fundamental result of Serfling [Ann. Statist. 2 (1974) 39-48], and further extend it to obtain a Bernstein concentration bound for sa","authors_text":"Odalric-Ambrym Maillard, R\\'emi Bardenet","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2013-09-16T16:38:20Z","title":"Concentration inequalities for sampling without replacement"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.4029","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:1930b3d041ab0547da08f60b9f9158d565740247af66ed9ac5998873706d78db","target":"record","created_at":"2026-05-18T01:36:21Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"6dca3a4ec54c859886fd3b2e3c1a966cc33adaa18606ba4a3c2a422aa41fb056","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2013-09-16T16:38:20Z","title_canon_sha256":"998be5c6268602c6ddb0855ae67994b70a97ffe7dd3cd8a7c48218e171aa1237"},"schema_version":"1.0","source":{"id":"1309.4029","kind":"arxiv","version":2}},"canonical_sha256":"bbbd7f1e131965df3a2d2c7dee398c1e3beff4e350ade206c0a275cb50de6187","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bbbd7f1e131965df3a2d2c7dee398c1e3beff4e350ade206c0a275cb50de6187","first_computed_at":"2026-05-18T01:36:21.021664Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:36:21.021664Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"x/Aew6ZFzpKlXLjMbpUh8jZS0LQFi3adKZ/ivKzrUf1+AmejDW++uEa6Y1fqqzCmUvPv5zDhy+atNyk2qoUtAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:36:21.022206Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.4029","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1930b3d041ab0547da08f60b9f9158d565740247af66ed9ac5998873706d78db","sha256:d236106aa1c8b5006e025749fb7e73e3314edf34f3a5f71a32c31cbdc743cb02"],"state_sha256":"a09bd155e661a3118d6c435e521afddef5d2c66ca5b741ced7609ff48fa0ab7e"}