{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:DZFYMIBBBMXN3R2NRU6MOEXD4S","short_pith_number":"pith:DZFYMIBB","schema_version":"1.0","canonical_sha256":"1e4b8620210b2eddc74d8d3cc712e3e484bb1692ba5499a2ee0c1a6cd85dbb75","source":{"kind":"arxiv","id":"1401.3987","version":4},"attestation_state":"computed","paper":{"title":"Distribution of the largest root of a matrix for Roy's test in multivariate analysis of variance","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Marco Chiani","submitted_at":"2014-01-16T11:13:55Z","abstract_excerpt":"Let ${\\bf X, Y} $ denote two independent real Gaussian $\\mathsf{p} \\times \\mathsf{m}$ and $\\mathsf{p} \\times \\mathsf{n}$ matrices with $\\mathsf{m}, \\mathsf{n} \\geq \\mathsf{p}$, each constituted by zero mean i.i.d. columns with common covariance. The Roy's largest root criterion, used in multivariate analysis of variance (MANOVA), is based on the statistic of the largest eigenvalue, $\\Theta_1$, of ${\\bf{(A+B)}}^{-1} \\bf{B}$, where ${\\bf A =X X}^T$ and ${\\bf B =Y Y}^T$ are independent central Wishart matrices. We derive a new expression and efficient recursive formulas for the exact distribution"},"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":"1401.3987","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2014-01-16T11:13:55Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"8f487b5f2cccfa48d6f98514d259fd04acedd906e5dbbc5395e147b91c8bb13e","abstract_canon_sha256":"51eabd8ee368e42a441cfc607a30d0b64ed74d74e842286bbf1466634d25c288"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:47:29.817418Z","signature_b64":"v8ZOPJw9p7eGQ7TmYQz8lsWIZEEw6weYhiPHrnshALpGziA4YcJkCmx4d5Cblp4FuUZfOXYz7H0EUTnJRKGNCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1e4b8620210b2eddc74d8d3cc712e3e484bb1692ba5499a2ee0c1a6cd85dbb75","last_reissued_at":"2026-05-18T00:47:29.816994Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:47:29.816994Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Distribution of the largest root of a matrix for Roy's test in multivariate analysis of variance","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Marco Chiani","submitted_at":"2014-01-16T11:13:55Z","abstract_excerpt":"Let ${\\bf X, Y} $ denote two independent real Gaussian $\\mathsf{p} \\times \\mathsf{m}$ and $\\mathsf{p} \\times \\mathsf{n}$ matrices with $\\mathsf{m}, \\mathsf{n} \\geq \\mathsf{p}$, each constituted by zero mean i.i.d. columns with common covariance. The Roy's largest root criterion, used in multivariate analysis of variance (MANOVA), is based on the statistic of the largest eigenvalue, $\\Theta_1$, of ${\\bf{(A+B)}}^{-1} \\bf{B}$, where ${\\bf A =X X}^T$ and ${\\bf B =Y Y}^T$ are independent central Wishart matrices. We derive a new expression and efficient recursive formulas for the exact distribution"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.3987","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":"1401.3987","created_at":"2026-05-18T00:47:29.817055+00:00"},{"alias_kind":"arxiv_version","alias_value":"1401.3987v4","created_at":"2026-05-18T00:47:29.817055+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.3987","created_at":"2026-05-18T00:47:29.817055+00:00"},{"alias_kind":"pith_short_12","alias_value":"DZFYMIBBBMXN","created_at":"2026-05-18T12:28:25.294606+00:00"},{"alias_kind":"pith_short_16","alias_value":"DZFYMIBBBMXN3R2N","created_at":"2026-05-18T12:28:25.294606+00:00"},{"alias_kind":"pith_short_8","alias_value":"DZFYMIBB","created_at":"2026-05-18T12:28:25.294606+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/DZFYMIBBBMXN3R2NRU6MOEXD4S","json":"https://pith.science/pith/DZFYMIBBBMXN3R2NRU6MOEXD4S.json","graph_json":"https://pith.science/api/pith-number/DZFYMIBBBMXN3R2NRU6MOEXD4S/graph.json","events_json":"https://pith.science/api/pith-number/DZFYMIBBBMXN3R2NRU6MOEXD4S/events.json","paper":"https://pith.science/paper/DZFYMIBB"},"agent_actions":{"view_html":"https://pith.science/pith/DZFYMIBBBMXN3R2NRU6MOEXD4S","download_json":"https://pith.science/pith/DZFYMIBBBMXN3R2NRU6MOEXD4S.json","view_paper":"https://pith.science/paper/DZFYMIBB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1401.3987&json=true","fetch_graph":"https://pith.science/api/pith-number/DZFYMIBBBMXN3R2NRU6MOEXD4S/graph.json","fetch_events":"https://pith.science/api/pith-number/DZFYMIBBBMXN3R2NRU6MOEXD4S/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DZFYMIBBBMXN3R2NRU6MOEXD4S/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DZFYMIBBBMXN3R2NRU6MOEXD4S/action/storage_attestation","attest_author":"https://pith.science/pith/DZFYMIBBBMXN3R2NRU6MOEXD4S/action/author_attestation","sign_citation":"https://pith.science/pith/DZFYMIBBBMXN3R2NRU6MOEXD4S/action/citation_signature","submit_replication":"https://pith.science/pith/DZFYMIBBBMXN3R2NRU6MOEXD4S/action/replication_record"}},"created_at":"2026-05-18T00:47:29.817055+00:00","updated_at":"2026-05-18T00:47:29.817055+00:00"}