{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:WCWBOBXCJGGTGWQE57YUOIZQCV","short_pith_number":"pith:WCWBOBXC","schema_version":"1.0","canonical_sha256":"b0ac1706e2498d335a04eff14723301567fed8fa537ddeabd6e5e98003922c60","source":{"kind":"arxiv","id":"1410.4726","version":2},"attestation_state":"computed","paper":{"title":"Nonparametric Stein-type Shrinkage Covariance Matrix Estimators in High-Dimensional Settings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.ME","authors_text":"Anestis Touloumis","submitted_at":"2014-10-17T14:01:04Z","abstract_excerpt":"Estimating a covariance matrix is an important task in applications where the number of variables is larger than the number of observations. Shrinkage approaches for estimating a high-dimensional covariance matrix are often employed to circumvent the limitations of the sample covariance matrix. A new family of nonparametric Stein-type shrinkage covariance estimators is proposed whose members are written as a convex linear combination of the sample covariance matrix and of a predefined invertible target matrix. Under the Frobenius norm criterion, the optimal shrinkage intensity that defines the"},"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":"1410.4726","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2014-10-17T14:01:04Z","cross_cats_sorted":[],"title_canon_sha256":"b92223af337c007bebda5adf0a1ee68b3e4903992d7a6a4175caf4f28f401797","abstract_canon_sha256":"86db6f83950abfcf80a8c6f0c37ce59594e1f241ffebe96800ad74e2574ff8d6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:46:13.995918Z","signature_b64":"4UAd/tqaNzBHY65YTkDyhuaBIN31B4B9avLhF8gwoxpeRzTzgzYX5Wz44TGDJVlj6cHsTiWoWbENy9jSxb3+AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b0ac1706e2498d335a04eff14723301567fed8fa537ddeabd6e5e98003922c60","last_reissued_at":"2026-05-18T01:46:13.995053Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:46:13.995053Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Nonparametric Stein-type Shrinkage Covariance Matrix Estimators in High-Dimensional Settings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.ME","authors_text":"Anestis Touloumis","submitted_at":"2014-10-17T14:01:04Z","abstract_excerpt":"Estimating a covariance matrix is an important task in applications where the number of variables is larger than the number of observations. Shrinkage approaches for estimating a high-dimensional covariance matrix are often employed to circumvent the limitations of the sample covariance matrix. A new family of nonparametric Stein-type shrinkage covariance estimators is proposed whose members are written as a convex linear combination of the sample covariance matrix and of a predefined invertible target matrix. Under the Frobenius norm criterion, the optimal shrinkage intensity that defines the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.4726","kind":"arxiv","version":2},"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":"1410.4726","created_at":"2026-05-18T01:46:13.995210+00:00"},{"alias_kind":"arxiv_version","alias_value":"1410.4726v2","created_at":"2026-05-18T01:46:13.995210+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.4726","created_at":"2026-05-18T01:46:13.995210+00:00"},{"alias_kind":"pith_short_12","alias_value":"WCWBOBXCJGGT","created_at":"2026-05-18T12:28:54.890064+00:00"},{"alias_kind":"pith_short_16","alias_value":"WCWBOBXCJGGTGWQE","created_at":"2026-05-18T12:28:54.890064+00:00"},{"alias_kind":"pith_short_8","alias_value":"WCWBOBXC","created_at":"2026-05-18T12:28:54.890064+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/WCWBOBXCJGGTGWQE57YUOIZQCV","json":"https://pith.science/pith/WCWBOBXCJGGTGWQE57YUOIZQCV.json","graph_json":"https://pith.science/api/pith-number/WCWBOBXCJGGTGWQE57YUOIZQCV/graph.json","events_json":"https://pith.science/api/pith-number/WCWBOBXCJGGTGWQE57YUOIZQCV/events.json","paper":"https://pith.science/paper/WCWBOBXC"},"agent_actions":{"view_html":"https://pith.science/pith/WCWBOBXCJGGTGWQE57YUOIZQCV","download_json":"https://pith.science/pith/WCWBOBXCJGGTGWQE57YUOIZQCV.json","view_paper":"https://pith.science/paper/WCWBOBXC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1410.4726&json=true","fetch_graph":"https://pith.science/api/pith-number/WCWBOBXCJGGTGWQE57YUOIZQCV/graph.json","fetch_events":"https://pith.science/api/pith-number/WCWBOBXCJGGTGWQE57YUOIZQCV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WCWBOBXCJGGTGWQE57YUOIZQCV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WCWBOBXCJGGTGWQE57YUOIZQCV/action/storage_attestation","attest_author":"https://pith.science/pith/WCWBOBXCJGGTGWQE57YUOIZQCV/action/author_attestation","sign_citation":"https://pith.science/pith/WCWBOBXCJGGTGWQE57YUOIZQCV/action/citation_signature","submit_replication":"https://pith.science/pith/WCWBOBXCJGGTGWQE57YUOIZQCV/action/replication_record"}},"created_at":"2026-05-18T01:46:13.995210+00:00","updated_at":"2026-05-18T01:46:13.995210+00:00"}