{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:MBJJA7XFBGYNM4O4TDFDBZ4732","short_pith_number":"pith:MBJJA7XF","schema_version":"1.0","canonical_sha256":"6052907ee509b0d671dc98ca30e79fdeb885b4dc215d81408eb36c65fde8fd97","source":{"kind":"arxiv","id":"1810.02088","version":1},"attestation_state":"computed","paper":{"title":"A Gaussian sequence approach for proving minimaxity: A Review","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"William E. Strawderman, Yuzo Maruyama","submitted_at":"2018-10-04T08:11:32Z","abstract_excerpt":"This paper reviews minimax best equivariant estimation in these invariant estimation problems: a location parameter, a scale parameter and a (Wishart) covariance matrix. We briefly review development of the best equivariant estimator as a generalized Bayes estimator relative to right invariant Haar measure in each case. Then we prove minimaxity of the best equivariant procedure by giving a least favorable prior sequence based on non-truncated Gaussian distributions. The results in this paper are all known, but we bring a fresh and somewhat unified approach by using, in contrast to most proofs "},"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":"1810.02088","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2018-10-04T08:11:32Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"98dd011ca262c03408215fcc9cbb6b56ca8d2ace29f8e5ca33158989b0f12afa","abstract_canon_sha256":"b82cfdd2a7584673a16e14b67d30604a9a9fd83147784167214e31f2dcceee02"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:04:06.314854Z","signature_b64":"jIDiPV3QWpY5GCmIdkIUVIrijcO4euYotIDCgY2mtHhY8G3V86a+rfP7fUEvgQL83ZXjLopvVm4vZoxws/wLAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6052907ee509b0d671dc98ca30e79fdeb885b4dc215d81408eb36c65fde8fd97","last_reissued_at":"2026-05-18T00:04:06.314227Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:04:06.314227Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Gaussian sequence approach for proving minimaxity: A Review","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"William E. Strawderman, Yuzo Maruyama","submitted_at":"2018-10-04T08:11:32Z","abstract_excerpt":"This paper reviews minimax best equivariant estimation in these invariant estimation problems: a location parameter, a scale parameter and a (Wishart) covariance matrix. We briefly review development of the best equivariant estimator as a generalized Bayes estimator relative to right invariant Haar measure in each case. Then we prove minimaxity of the best equivariant procedure by giving a least favorable prior sequence based on non-truncated Gaussian distributions. The results in this paper are all known, but we bring a fresh and somewhat unified approach by using, in contrast to most proofs "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.02088","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":"1810.02088","created_at":"2026-05-18T00:04:06.314340+00:00"},{"alias_kind":"arxiv_version","alias_value":"1810.02088v1","created_at":"2026-05-18T00:04:06.314340+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.02088","created_at":"2026-05-18T00:04:06.314340+00:00"},{"alias_kind":"pith_short_12","alias_value":"MBJJA7XFBGYN","created_at":"2026-05-18T12:32:37.024351+00:00"},{"alias_kind":"pith_short_16","alias_value":"MBJJA7XFBGYNM4O4","created_at":"2026-05-18T12:32:37.024351+00:00"},{"alias_kind":"pith_short_8","alias_value":"MBJJA7XF","created_at":"2026-05-18T12:32:37.024351+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/MBJJA7XFBGYNM4O4TDFDBZ4732","json":"https://pith.science/pith/MBJJA7XFBGYNM4O4TDFDBZ4732.json","graph_json":"https://pith.science/api/pith-number/MBJJA7XFBGYNM4O4TDFDBZ4732/graph.json","events_json":"https://pith.science/api/pith-number/MBJJA7XFBGYNM4O4TDFDBZ4732/events.json","paper":"https://pith.science/paper/MBJJA7XF"},"agent_actions":{"view_html":"https://pith.science/pith/MBJJA7XFBGYNM4O4TDFDBZ4732","download_json":"https://pith.science/pith/MBJJA7XFBGYNM4O4TDFDBZ4732.json","view_paper":"https://pith.science/paper/MBJJA7XF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1810.02088&json=true","fetch_graph":"https://pith.science/api/pith-number/MBJJA7XFBGYNM4O4TDFDBZ4732/graph.json","fetch_events":"https://pith.science/api/pith-number/MBJJA7XFBGYNM4O4TDFDBZ4732/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MBJJA7XFBGYNM4O4TDFDBZ4732/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MBJJA7XFBGYNM4O4TDFDBZ4732/action/storage_attestation","attest_author":"https://pith.science/pith/MBJJA7XFBGYNM4O4TDFDBZ4732/action/author_attestation","sign_citation":"https://pith.science/pith/MBJJA7XFBGYNM4O4TDFDBZ4732/action/citation_signature","submit_replication":"https://pith.science/pith/MBJJA7XFBGYNM4O4TDFDBZ4732/action/replication_record"}},"created_at":"2026-05-18T00:04:06.314340+00:00","updated_at":"2026-05-18T00:04:06.314340+00:00"}