{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:NZG75NEOMZASK3KBE6GMRDCGFF","short_pith_number":"pith:NZG75NEO","schema_version":"1.0","canonical_sha256":"6e4dfeb48e6641256d41278cc88c4629541620157ef5ae560810017205e51452","source":{"kind":"arxiv","id":"1408.0424","version":1},"attestation_state":"computed","paper":{"title":"Equivariant minimax dominators of the MLE in the array normal model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"David Gerard, Peter Hoff","submitted_at":"2014-08-02T21:40:22Z","abstract_excerpt":"Inference about dependencies in a multiway data array can be made using the array normal model, which corresponds to the class of multivariate normal distributions with separable covariance matrices. Maximum likelihood and Bayesian methods for inference in the array normal model have appeared in the literature, but there have not been any results concerning the optimality properties of such estimators. In this article, we obtain results for the array normal model that are analogous to some classical results concerning covariance estimation for the multivariate normal model. We show that under "},"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":"1408.0424","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2014-08-02T21:40:22Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"ad1f2ae575a8095b7c4f6cfae405f8a037540e61e388a78434de879d39ede17f","abstract_canon_sha256":"9c1399aa331f2346d4b06585bf95c7d088a9b3fc84f9e2fe41847717ae3145e9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:12:58.902437Z","signature_b64":"3KLOXuuQBru9J0hfM+1ZezFcyu/VPhZltQMN0QWt9cyBjMvybjy2Yc5IQCKaa484EgXP23oLtwMxA6+H6uy5DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6e4dfeb48e6641256d41278cc88c4629541620157ef5ae560810017205e51452","last_reissued_at":"2026-05-18T00:12:58.901920Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:12:58.901920Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Equivariant minimax dominators of the MLE in the array normal model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"David Gerard, Peter Hoff","submitted_at":"2014-08-02T21:40:22Z","abstract_excerpt":"Inference about dependencies in a multiway data array can be made using the array normal model, which corresponds to the class of multivariate normal distributions with separable covariance matrices. Maximum likelihood and Bayesian methods for inference in the array normal model have appeared in the literature, but there have not been any results concerning the optimality properties of such estimators. In this article, we obtain results for the array normal model that are analogous to some classical results concerning covariance estimation for the multivariate normal model. We show that under "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.0424","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":"1408.0424","created_at":"2026-05-18T00:12:58.901990+00:00"},{"alias_kind":"arxiv_version","alias_value":"1408.0424v1","created_at":"2026-05-18T00:12:58.901990+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.0424","created_at":"2026-05-18T00:12:58.901990+00:00"},{"alias_kind":"pith_short_12","alias_value":"NZG75NEOMZAS","created_at":"2026-05-18T12:28:41.024544+00:00"},{"alias_kind":"pith_short_16","alias_value":"NZG75NEOMZASK3KB","created_at":"2026-05-18T12:28:41.024544+00:00"},{"alias_kind":"pith_short_8","alias_value":"NZG75NEO","created_at":"2026-05-18T12:28:41.024544+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/NZG75NEOMZASK3KBE6GMRDCGFF","json":"https://pith.science/pith/NZG75NEOMZASK3KBE6GMRDCGFF.json","graph_json":"https://pith.science/api/pith-number/NZG75NEOMZASK3KBE6GMRDCGFF/graph.json","events_json":"https://pith.science/api/pith-number/NZG75NEOMZASK3KBE6GMRDCGFF/events.json","paper":"https://pith.science/paper/NZG75NEO"},"agent_actions":{"view_html":"https://pith.science/pith/NZG75NEOMZASK3KBE6GMRDCGFF","download_json":"https://pith.science/pith/NZG75NEOMZASK3KBE6GMRDCGFF.json","view_paper":"https://pith.science/paper/NZG75NEO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1408.0424&json=true","fetch_graph":"https://pith.science/api/pith-number/NZG75NEOMZASK3KBE6GMRDCGFF/graph.json","fetch_events":"https://pith.science/api/pith-number/NZG75NEOMZASK3KBE6GMRDCGFF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NZG75NEOMZASK3KBE6GMRDCGFF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NZG75NEOMZASK3KBE6GMRDCGFF/action/storage_attestation","attest_author":"https://pith.science/pith/NZG75NEOMZASK3KBE6GMRDCGFF/action/author_attestation","sign_citation":"https://pith.science/pith/NZG75NEOMZASK3KBE6GMRDCGFF/action/citation_signature","submit_replication":"https://pith.science/pith/NZG75NEOMZASK3KBE6GMRDCGFF/action/replication_record"}},"created_at":"2026-05-18T00:12:58.901990+00:00","updated_at":"2026-05-18T00:12:58.901990+00:00"}