{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:5GK7RVFFZ3FKCH27AGPAJBXHOW","short_pith_number":"pith:5GK7RVFF","schema_version":"1.0","canonical_sha256":"e995f8d4a5cecaa11f5f019e0486e775a9e3295f73fbf7edad4e678e2c8a954d","source":{"kind":"arxiv","id":"1301.2677","version":4},"attestation_state":"computed","paper":{"title":"EM algorithms for estimating the Bernstein copula","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.CO","authors_text":"Donald Richards, Gwo Dong Lin, Satoshi Kuriki, Xiaoling Dou","submitted_at":"2013-01-12T11:44:14Z","abstract_excerpt":"A method that uses order statistics to construct multivariate distributions with fixed marginals and which utilizes a representation of the Bernstein copula in terms of a finite mixture distribution is proposed. Expectation-maximization (EM) algorithms to estimate the Bernstein copula are proposed, and a local convergence property is proved. Moreover, asymptotic properties of the proposed semiparametric estimators are provided. Illustrative examples are presented using three real data sets and a 3-dimensional simulated data set. These studies show that the Bernstein copula is able to represent"},"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":"1301.2677","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.CO","submitted_at":"2013-01-12T11:44:14Z","cross_cats_sorted":[],"title_canon_sha256":"b9f48d520faf0c83807a01cb3d44ea9060e23f1287ee44a0fd5024d35f22df0a","abstract_canon_sha256":"3340ef980c77e8072421b725f85679b3e45796e7585ba28f820d36b4c5ba6587"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:02:17.779673Z","signature_b64":"wT86VLMoTBOAae30vZR9b64prbMyUF92+4iBMkmb3hQggVZkPtilYIU9rRkJN5txmZWFmnWkqyuy60FsWkc9Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e995f8d4a5cecaa11f5f019e0486e775a9e3295f73fbf7edad4e678e2c8a954d","last_reissued_at":"2026-05-18T03:02:17.778836Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:02:17.778836Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"EM algorithms for estimating the Bernstein copula","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.CO","authors_text":"Donald Richards, Gwo Dong Lin, Satoshi Kuriki, Xiaoling Dou","submitted_at":"2013-01-12T11:44:14Z","abstract_excerpt":"A method that uses order statistics to construct multivariate distributions with fixed marginals and which utilizes a representation of the Bernstein copula in terms of a finite mixture distribution is proposed. Expectation-maximization (EM) algorithms to estimate the Bernstein copula are proposed, and a local convergence property is proved. Moreover, asymptotic properties of the proposed semiparametric estimators are provided. Illustrative examples are presented using three real data sets and a 3-dimensional simulated data set. These studies show that the Bernstein copula is able to represent"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.2677","kind":"arxiv","version":4},"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":"1301.2677","created_at":"2026-05-18T03:02:17.778958+00:00"},{"alias_kind":"arxiv_version","alias_value":"1301.2677v4","created_at":"2026-05-18T03:02:17.778958+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.2677","created_at":"2026-05-18T03:02:17.778958+00:00"},{"alias_kind":"pith_short_12","alias_value":"5GK7RVFFZ3FK","created_at":"2026-05-18T12:27:34.582898+00:00"},{"alias_kind":"pith_short_16","alias_value":"5GK7RVFFZ3FKCH27","created_at":"2026-05-18T12:27:34.582898+00:00"},{"alias_kind":"pith_short_8","alias_value":"5GK7RVFF","created_at":"2026-05-18T12:27:34.582898+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/5GK7RVFFZ3FKCH27AGPAJBXHOW","json":"https://pith.science/pith/5GK7RVFFZ3FKCH27AGPAJBXHOW.json","graph_json":"https://pith.science/api/pith-number/5GK7RVFFZ3FKCH27AGPAJBXHOW/graph.json","events_json":"https://pith.science/api/pith-number/5GK7RVFFZ3FKCH27AGPAJBXHOW/events.json","paper":"https://pith.science/paper/5GK7RVFF"},"agent_actions":{"view_html":"https://pith.science/pith/5GK7RVFFZ3FKCH27AGPAJBXHOW","download_json":"https://pith.science/pith/5GK7RVFFZ3FKCH27AGPAJBXHOW.json","view_paper":"https://pith.science/paper/5GK7RVFF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1301.2677&json=true","fetch_graph":"https://pith.science/api/pith-number/5GK7RVFFZ3FKCH27AGPAJBXHOW/graph.json","fetch_events":"https://pith.science/api/pith-number/5GK7RVFFZ3FKCH27AGPAJBXHOW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5GK7RVFFZ3FKCH27AGPAJBXHOW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5GK7RVFFZ3FKCH27AGPAJBXHOW/action/storage_attestation","attest_author":"https://pith.science/pith/5GK7RVFFZ3FKCH27AGPAJBXHOW/action/author_attestation","sign_citation":"https://pith.science/pith/5GK7RVFFZ3FKCH27AGPAJBXHOW/action/citation_signature","submit_replication":"https://pith.science/pith/5GK7RVFFZ3FKCH27AGPAJBXHOW/action/replication_record"}},"created_at":"2026-05-18T03:02:17.778958+00:00","updated_at":"2026-05-18T03:02:17.778958+00:00"}