{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:3L4LUWY4U547OWJVY44KYBHSI5","short_pith_number":"pith:3L4LUWY4","schema_version":"1.0","canonical_sha256":"daf8ba5b1ca779f75935c738ac04f2476952243d72a19d2f946c341d7f74a579","source":{"kind":"arxiv","id":"1504.03506","version":1},"attestation_state":"computed","paper":{"title":"Minimax rates for finite mixture estimation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Jonas Kahn, Philippe Heinrich","submitted_at":"2015-04-14T12:03:27Z","abstract_excerpt":"We prove that under some regularity and strong identifiability conditions, around a mixing distribution with $m_0$ components, the optimal local minimax rate of estimation of a mixture with $m$ components is $n^{-1/(4(m-m_0) + 2)}$. This corrects a previous paper by Chen (1995) in The Annals of Statistics."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1504.03506","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2015-04-14T12:03:27Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"7f9b75f0975a3eae05992743968f50c362ac7716bf1f361dea4367a6f3d9bcfb","abstract_canon_sha256":"55bbcf41d866e0a374cb47c66f22ef61066ffa99d52063b610a2b86fde4919d0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:18:50.695789Z","signature_b64":"i3pV2qo0XsvQOripscitA8xx34MjaU1jtN24AbykbT4Y4bFvgMJBIst1/47MOR8dcCJVy2jiHQlcitV1aODLCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"daf8ba5b1ca779f75935c738ac04f2476952243d72a19d2f946c341d7f74a579","last_reissued_at":"2026-05-18T02:18:50.695069Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:18:50.695069Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Minimax rates for finite mixture estimation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Jonas Kahn, Philippe Heinrich","submitted_at":"2015-04-14T12:03:27Z","abstract_excerpt":"We prove that under some regularity and strong identifiability conditions, around a mixing distribution with $m_0$ components, the optimal local minimax rate of estimation of a mixture with $m$ components is $n^{-1/(4(m-m_0) + 2)}$. This corrects a previous paper by Chen (1995) in The Annals of Statistics."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.03506","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":""},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1504.03506","created_at":"2026-05-18T02:18:50.695168+00:00"},{"alias_kind":"arxiv_version","alias_value":"1504.03506v1","created_at":"2026-05-18T02:18:50.695168+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.03506","created_at":"2026-05-18T02:18:50.695168+00:00"},{"alias_kind":"pith_short_12","alias_value":"3L4LUWY4U547","created_at":"2026-05-18T12:29:02.477457+00:00"},{"alias_kind":"pith_short_16","alias_value":"3L4LUWY4U547OWJV","created_at":"2026-05-18T12:29:02.477457+00:00"},{"alias_kind":"pith_short_8","alias_value":"3L4LUWY4","created_at":"2026-05-18T12:29:02.477457+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/3L4LUWY4U547OWJVY44KYBHSI5","json":"https://pith.science/pith/3L4LUWY4U547OWJVY44KYBHSI5.json","graph_json":"https://pith.science/api/pith-number/3L4LUWY4U547OWJVY44KYBHSI5/graph.json","events_json":"https://pith.science/api/pith-number/3L4LUWY4U547OWJVY44KYBHSI5/events.json","paper":"https://pith.science/paper/3L4LUWY4"},"agent_actions":{"view_html":"https://pith.science/pith/3L4LUWY4U547OWJVY44KYBHSI5","download_json":"https://pith.science/pith/3L4LUWY4U547OWJVY44KYBHSI5.json","view_paper":"https://pith.science/paper/3L4LUWY4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1504.03506&json=true","fetch_graph":"https://pith.science/api/pith-number/3L4LUWY4U547OWJVY44KYBHSI5/graph.json","fetch_events":"https://pith.science/api/pith-number/3L4LUWY4U547OWJVY44KYBHSI5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3L4LUWY4U547OWJVY44KYBHSI5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3L4LUWY4U547OWJVY44KYBHSI5/action/storage_attestation","attest_author":"https://pith.science/pith/3L4LUWY4U547OWJVY44KYBHSI5/action/author_attestation","sign_citation":"https://pith.science/pith/3L4LUWY4U547OWJVY44KYBHSI5/action/citation_signature","submit_replication":"https://pith.science/pith/3L4LUWY4U547OWJVY44KYBHSI5/action/replication_record"}},"created_at":"2026-05-18T02:18:50.695168+00:00","updated_at":"2026-05-18T02:18:50.695168+00:00"}