{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:QV27IVD2Q2WK7HES7CXQMP2WXH","short_pith_number":"pith:QV27IVD2","schema_version":"1.0","canonical_sha256":"8575f4547a86acaf9c92f8af063f56b9cf81fa8c86eb39d50ba7286fe4b2e2a7","source":{"kind":"arxiv","id":"1404.6633","version":1},"attestation_state":"computed","paper":{"title":"Substitution principle for CLT of linear spectral statistics of high-dimensional sample covariance matrices with applications to hypothesis testing","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.ME","authors_text":"Jiangfeng Yao, Shurong Zheng, Z. D. Bai","submitted_at":"2014-04-26T10:56:58Z","abstract_excerpt":"Sample covariance matrices are widely used in multivariate statistical analysis. The central limit theorems (CLT's) for linear spectral statistics of high-dimensional non-centered sample covariance matrices have received considerable attention in random matrix theory and have been applied to many high-dimensional statistical problems. However, known population mean vectors are assumed for non-centered sample covariance matrices, some of which even assume Gaussian-like moment conditions. In fact, there are still another two most frequently used sample covariance matrices: the MLE (by subtractin"},"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":"1404.6633","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2014-04-26T10:56:58Z","cross_cats_sorted":[],"title_canon_sha256":"4407fd63a0d7cce8b251a437780f8152dab57d46350c785cd7b5277440c47a75","abstract_canon_sha256":"2886bf730d7b94806e331a3ebf86d6c2272ed86824e160c96efd83cd8a071792"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:53:06.435621Z","signature_b64":"S9SPG+m/YaPHoWFSTf8LYNauzPkAinjl8d7swHFe3lM56SnCv3b1umype4BLveI1ZjRlAmyy4CBZeLeYzmO6Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8575f4547a86acaf9c92f8af063f56b9cf81fa8c86eb39d50ba7286fe4b2e2a7","last_reissued_at":"2026-05-18T02:53:06.434797Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:53:06.434797Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Substitution principle for CLT of linear spectral statistics of high-dimensional sample covariance matrices with applications to hypothesis testing","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.ME","authors_text":"Jiangfeng Yao, Shurong Zheng, Z. D. Bai","submitted_at":"2014-04-26T10:56:58Z","abstract_excerpt":"Sample covariance matrices are widely used in multivariate statistical analysis. The central limit theorems (CLT's) for linear spectral statistics of high-dimensional non-centered sample covariance matrices have received considerable attention in random matrix theory and have been applied to many high-dimensional statistical problems. However, known population mean vectors are assumed for non-centered sample covariance matrices, some of which even assume Gaussian-like moment conditions. In fact, there are still another two most frequently used sample covariance matrices: the MLE (by subtractin"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.6633","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":"1404.6633","created_at":"2026-05-18T02:53:06.434918+00:00"},{"alias_kind":"arxiv_version","alias_value":"1404.6633v1","created_at":"2026-05-18T02:53:06.434918+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.6633","created_at":"2026-05-18T02:53:06.434918+00:00"},{"alias_kind":"pith_short_12","alias_value":"QV27IVD2Q2WK","created_at":"2026-05-18T12:28:46.137349+00:00"},{"alias_kind":"pith_short_16","alias_value":"QV27IVD2Q2WK7HES","created_at":"2026-05-18T12:28:46.137349+00:00"},{"alias_kind":"pith_short_8","alias_value":"QV27IVD2","created_at":"2026-05-18T12:28:46.137349+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/QV27IVD2Q2WK7HES7CXQMP2WXH","json":"https://pith.science/pith/QV27IVD2Q2WK7HES7CXQMP2WXH.json","graph_json":"https://pith.science/api/pith-number/QV27IVD2Q2WK7HES7CXQMP2WXH/graph.json","events_json":"https://pith.science/api/pith-number/QV27IVD2Q2WK7HES7CXQMP2WXH/events.json","paper":"https://pith.science/paper/QV27IVD2"},"agent_actions":{"view_html":"https://pith.science/pith/QV27IVD2Q2WK7HES7CXQMP2WXH","download_json":"https://pith.science/pith/QV27IVD2Q2WK7HES7CXQMP2WXH.json","view_paper":"https://pith.science/paper/QV27IVD2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1404.6633&json=true","fetch_graph":"https://pith.science/api/pith-number/QV27IVD2Q2WK7HES7CXQMP2WXH/graph.json","fetch_events":"https://pith.science/api/pith-number/QV27IVD2Q2WK7HES7CXQMP2WXH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QV27IVD2Q2WK7HES7CXQMP2WXH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QV27IVD2Q2WK7HES7CXQMP2WXH/action/storage_attestation","attest_author":"https://pith.science/pith/QV27IVD2Q2WK7HES7CXQMP2WXH/action/author_attestation","sign_citation":"https://pith.science/pith/QV27IVD2Q2WK7HES7CXQMP2WXH/action/citation_signature","submit_replication":"https://pith.science/pith/QV27IVD2Q2WK7HES7CXQMP2WXH/action/replication_record"}},"created_at":"2026-05-18T02:53:06.434918+00:00","updated_at":"2026-05-18T02:53:06.434918+00:00"}