{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:DARHUAFD654UBGWYEWAELQMYTV","short_pith_number":"pith:DARHUAFD","schema_version":"1.0","canonical_sha256":"18227a00a3f779409ad8258045c1989d50c16761d2e8562526804a8f6bad3fd8","source":{"kind":"arxiv","id":"1507.08377","version":1},"attestation_state":"computed","paper":{"title":"Large Covariance Estimation through Elliptical Factor Models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.ME","authors_text":"Han Liu, Jianqing Fan, Weichen Wang","submitted_at":"2015-07-30T05:02:46Z","abstract_excerpt":"We proposed a general Principal Orthogonal complEment Thresholding (POET) framework for large-scale covariance matrix estimation based on an approximate factor model. A set of high level sufficient conditions for the procedure to achieve optimal rates of convergence under different matrix norms were brought up to better understand how POET works. Such a framework allows us to recover the results for sub-Gaussian in a more transparent way that only depends on the concentration properties of the sample covariance matrix. As a new theoretical contribution, for the first time, such a framework all"},"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":"1507.08377","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2015-07-30T05:02:46Z","cross_cats_sorted":[],"title_canon_sha256":"e9601eb0b1b06f8b78334f4637f233a5e088dbd6670848522b5e929b54c1229f","abstract_canon_sha256":"3dcf71f50f1b9a30791573e0162c572f3ac365c7b69f6fb2cbe393d9056c36fc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:36:06.644836Z","signature_b64":"uwx/BvVmu0Bq6AhadFqEuSKh8HDBdE9n0P1L/e52v32TDVBAjJ2eyeGcc+3DQE0Jl7GkCM9IinwEw9ZgHPyfBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"18227a00a3f779409ad8258045c1989d50c16761d2e8562526804a8f6bad3fd8","last_reissued_at":"2026-05-18T01:36:06.644324Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:36:06.644324Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Large Covariance Estimation through Elliptical Factor Models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.ME","authors_text":"Han Liu, Jianqing Fan, Weichen Wang","submitted_at":"2015-07-30T05:02:46Z","abstract_excerpt":"We proposed a general Principal Orthogonal complEment Thresholding (POET) framework for large-scale covariance matrix estimation based on an approximate factor model. A set of high level sufficient conditions for the procedure to achieve optimal rates of convergence under different matrix norms were brought up to better understand how POET works. Such a framework allows us to recover the results for sub-Gaussian in a more transparent way that only depends on the concentration properties of the sample covariance matrix. As a new theoretical contribution, for the first time, such a framework all"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.08377","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":"1507.08377","created_at":"2026-05-18T01:36:06.644405+00:00"},{"alias_kind":"arxiv_version","alias_value":"1507.08377v1","created_at":"2026-05-18T01:36:06.644405+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.08377","created_at":"2026-05-18T01:36:06.644405+00:00"},{"alias_kind":"pith_short_12","alias_value":"DARHUAFD654U","created_at":"2026-05-18T12:29:17.054201+00:00"},{"alias_kind":"pith_short_16","alias_value":"DARHUAFD654UBGWY","created_at":"2026-05-18T12:29:17.054201+00:00"},{"alias_kind":"pith_short_8","alias_value":"DARHUAFD","created_at":"2026-05-18T12:29:17.054201+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/DARHUAFD654UBGWYEWAELQMYTV","json":"https://pith.science/pith/DARHUAFD654UBGWYEWAELQMYTV.json","graph_json":"https://pith.science/api/pith-number/DARHUAFD654UBGWYEWAELQMYTV/graph.json","events_json":"https://pith.science/api/pith-number/DARHUAFD654UBGWYEWAELQMYTV/events.json","paper":"https://pith.science/paper/DARHUAFD"},"agent_actions":{"view_html":"https://pith.science/pith/DARHUAFD654UBGWYEWAELQMYTV","download_json":"https://pith.science/pith/DARHUAFD654UBGWYEWAELQMYTV.json","view_paper":"https://pith.science/paper/DARHUAFD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1507.08377&json=true","fetch_graph":"https://pith.science/api/pith-number/DARHUAFD654UBGWYEWAELQMYTV/graph.json","fetch_events":"https://pith.science/api/pith-number/DARHUAFD654UBGWYEWAELQMYTV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DARHUAFD654UBGWYEWAELQMYTV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DARHUAFD654UBGWYEWAELQMYTV/action/storage_attestation","attest_author":"https://pith.science/pith/DARHUAFD654UBGWYEWAELQMYTV/action/author_attestation","sign_citation":"https://pith.science/pith/DARHUAFD654UBGWYEWAELQMYTV/action/citation_signature","submit_replication":"https://pith.science/pith/DARHUAFD654UBGWYEWAELQMYTV/action/replication_record"}},"created_at":"2026-05-18T01:36:06.644405+00:00","updated_at":"2026-05-18T01:36:06.644405+00:00"}