{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:V7E3ERUNACMSJXXS37D3KUEAS5","short_pith_number":"pith:V7E3ERUN","schema_version":"1.0","canonical_sha256":"afc9b2468d009924def2dfc7b55080976ff0a60758514e2e99d1d5f24e7a3e2a","source":{"kind":"arxiv","id":"1507.04313","version":1},"attestation_state":"computed","paper":{"title":"Optimal 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":"2015-07-15T18:20:17Z","abstract_excerpt":"We study the rates of estimation of finite mixing distributions, that is, the parameters of the mixture. We prove that under some regularity and strong identifiability conditions, around a given mixing distribution with $m_0$ components, the optimal local minimax rate of estimation of a mixing distribution with $m$ components is $n^{-1/(4(m-m_0) + 2)}$. This corrects a previous paper by Chen (1995) in The Annals of Statistics.\n  By contrast, it turns out that there are estimators with a (non-uniform) pointwise rate of estimation of $n^{-1/2}$ for all mixing distributions with a finite number o"},"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":"1507.04313","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2015-07-15T18:20:17Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"d2df9b2499f1fb63f2b4acdb296a04f2849e18ec28c809ac91c9cb60254306aa","abstract_canon_sha256":"54737fac7addb5b3d9cdfbe49dbf5a535d3c291821e4ec33fc9c529814752271"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:36:48.684515Z","signature_b64":"jwlilsDsV3AEF/NyA/UzV/i06x9WNhm5GdGI/xtowWcqKdsI6z79NsHvoRE3FByCd2Sqru54jdgK6085dsEmBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"afc9b2468d009924def2dfc7b55080976ff0a60758514e2e99d1d5f24e7a3e2a","last_reissued_at":"2026-05-18T01:36:48.683801Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:36:48.683801Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Optimal 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":"2015-07-15T18:20:17Z","abstract_excerpt":"We study the rates of estimation of finite mixing distributions, that is, the parameters of the mixture. We prove that under some regularity and strong identifiability conditions, around a given mixing distribution with $m_0$ components, the optimal local minimax rate of estimation of a mixing distribution with $m$ components is $n^{-1/(4(m-m_0) + 2)}$. This corrects a previous paper by Chen (1995) in The Annals of Statistics.\n  By contrast, it turns out that there are estimators with a (non-uniform) pointwise rate of estimation of $n^{-1/2}$ for all mixing distributions with a finite number o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.04313","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":"1507.04313","created_at":"2026-05-18T01:36:48.683910+00:00"},{"alias_kind":"arxiv_version","alias_value":"1507.04313v1","created_at":"2026-05-18T01:36:48.683910+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.04313","created_at":"2026-05-18T01:36:48.683910+00:00"},{"alias_kind":"pith_short_12","alias_value":"V7E3ERUNACMS","created_at":"2026-05-18T12:29:44.643036+00:00"},{"alias_kind":"pith_short_16","alias_value":"V7E3ERUNACMSJXXS","created_at":"2026-05-18T12:29:44.643036+00:00"},{"alias_kind":"pith_short_8","alias_value":"V7E3ERUN","created_at":"2026-05-18T12:29:44.643036+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/V7E3ERUNACMSJXXS37D3KUEAS5","json":"https://pith.science/pith/V7E3ERUNACMSJXXS37D3KUEAS5.json","graph_json":"https://pith.science/api/pith-number/V7E3ERUNACMSJXXS37D3KUEAS5/graph.json","events_json":"https://pith.science/api/pith-number/V7E3ERUNACMSJXXS37D3KUEAS5/events.json","paper":"https://pith.science/paper/V7E3ERUN"},"agent_actions":{"view_html":"https://pith.science/pith/V7E3ERUNACMSJXXS37D3KUEAS5","download_json":"https://pith.science/pith/V7E3ERUNACMSJXXS37D3KUEAS5.json","view_paper":"https://pith.science/paper/V7E3ERUN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1507.04313&json=true","fetch_graph":"https://pith.science/api/pith-number/V7E3ERUNACMSJXXS37D3KUEAS5/graph.json","fetch_events":"https://pith.science/api/pith-number/V7E3ERUNACMSJXXS37D3KUEAS5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/V7E3ERUNACMSJXXS37D3KUEAS5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/V7E3ERUNACMSJXXS37D3KUEAS5/action/storage_attestation","attest_author":"https://pith.science/pith/V7E3ERUNACMSJXXS37D3KUEAS5/action/author_attestation","sign_citation":"https://pith.science/pith/V7E3ERUNACMSJXXS37D3KUEAS5/action/citation_signature","submit_replication":"https://pith.science/pith/V7E3ERUNACMSJXXS37D3KUEAS5/action/replication_record"}},"created_at":"2026-05-18T01:36:48.683910+00:00","updated_at":"2026-05-18T01:36:48.683910+00:00"}