{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:BQ5RI32L2EUDPU4JTXHZERPLKJ","short_pith_number":"pith:BQ5RI32L","schema_version":"1.0","canonical_sha256":"0c3b146f4bd12837d3899dcf9245eb5258a64cbeb390434e491463079d9c98d1","source":{"kind":"arxiv","id":"1706.10066","version":1},"attestation_state":"computed","paper":{"title":"Optimal High-Dimensional Shrinkage Covariance Estimation for Elliptical Distributions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.ME","authors_text":"Esa Ollila","submitted_at":"2017-06-30T08:49:00Z","abstract_excerpt":"We derive an optimal shrinkage sample covariance matrix (SCM) estimator which is suitable for high dimensional problems and when sampling from an unspecified elliptically symmetric distribution. Specifically, we derive the optimal (oracle) shrinkage parameters that obtain the minimum mean-squared error (MMSE) between the shrinkage SCM and the true covariance matrix when sampling from an elliptical distribution. Subsequently, we show how the oracle shrinkage parameters can be consistently estimated under the random matrix theory regime. Simulations show the advantage of the proposed estimator 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":"1706.10066","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2017-06-30T08:49:00Z","cross_cats_sorted":[],"title_canon_sha256":"261c31bd7c3e3c1a8a2bde7dc63bfa6b3108f8f68ccd62cfd090caba136c97f7","abstract_canon_sha256":"cd8becdedd6feab00e41e9260aecf961b6fdd3bc2c8ce188855bd2367a92d88e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:41:11.524725Z","signature_b64":"l5Jk9+gT/bSC4BSiLL79oWi4UVVbLiYKUKSiWiaJLtcqQPZ/gVXE9b8Ir/CeutlI2B7Tdm3QrQKF86LxK4m6Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0c3b146f4bd12837d3899dcf9245eb5258a64cbeb390434e491463079d9c98d1","last_reissued_at":"2026-05-18T00:41:11.524242Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:41:11.524242Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Optimal High-Dimensional Shrinkage Covariance Estimation for Elliptical Distributions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.ME","authors_text":"Esa Ollila","submitted_at":"2017-06-30T08:49:00Z","abstract_excerpt":"We derive an optimal shrinkage sample covariance matrix (SCM) estimator which is suitable for high dimensional problems and when sampling from an unspecified elliptically symmetric distribution. Specifically, we derive the optimal (oracle) shrinkage parameters that obtain the minimum mean-squared error (MMSE) between the shrinkage SCM and the true covariance matrix when sampling from an elliptical distribution. Subsequently, we show how the oracle shrinkage parameters can be consistently estimated under the random matrix theory regime. Simulations show the advantage of the proposed estimator o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.10066","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":"1706.10066","created_at":"2026-05-18T00:41:11.524311+00:00"},{"alias_kind":"arxiv_version","alias_value":"1706.10066v1","created_at":"2026-05-18T00:41:11.524311+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.10066","created_at":"2026-05-18T00:41:11.524311+00:00"},{"alias_kind":"pith_short_12","alias_value":"BQ5RI32L2EUD","created_at":"2026-05-18T12:31:08.081275+00:00"},{"alias_kind":"pith_short_16","alias_value":"BQ5RI32L2EUDPU4J","created_at":"2026-05-18T12:31:08.081275+00:00"},{"alias_kind":"pith_short_8","alias_value":"BQ5RI32L","created_at":"2026-05-18T12:31:08.081275+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/BQ5RI32L2EUDPU4JTXHZERPLKJ","json":"https://pith.science/pith/BQ5RI32L2EUDPU4JTXHZERPLKJ.json","graph_json":"https://pith.science/api/pith-number/BQ5RI32L2EUDPU4JTXHZERPLKJ/graph.json","events_json":"https://pith.science/api/pith-number/BQ5RI32L2EUDPU4JTXHZERPLKJ/events.json","paper":"https://pith.science/paper/BQ5RI32L"},"agent_actions":{"view_html":"https://pith.science/pith/BQ5RI32L2EUDPU4JTXHZERPLKJ","download_json":"https://pith.science/pith/BQ5RI32L2EUDPU4JTXHZERPLKJ.json","view_paper":"https://pith.science/paper/BQ5RI32L","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1706.10066&json=true","fetch_graph":"https://pith.science/api/pith-number/BQ5RI32L2EUDPU4JTXHZERPLKJ/graph.json","fetch_events":"https://pith.science/api/pith-number/BQ5RI32L2EUDPU4JTXHZERPLKJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BQ5RI32L2EUDPU4JTXHZERPLKJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BQ5RI32L2EUDPU4JTXHZERPLKJ/action/storage_attestation","attest_author":"https://pith.science/pith/BQ5RI32L2EUDPU4JTXHZERPLKJ/action/author_attestation","sign_citation":"https://pith.science/pith/BQ5RI32L2EUDPU4JTXHZERPLKJ/action/citation_signature","submit_replication":"https://pith.science/pith/BQ5RI32L2EUDPU4JTXHZERPLKJ/action/replication_record"}},"created_at":"2026-05-18T00:41:11.524311+00:00","updated_at":"2026-05-18T00:41:11.524311+00:00"}