{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:FOUHQ4KM5Z2UAHLYI7D7AGWNXM","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"6ac7f23c148f27382a5ba8d3fb9fe283bcc3c4586ac4453681336fea24fec2ac","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2012-05-18T19:06:15Z","title_canon_sha256":"03b42b14ca98a1e01bb805d8923a59e1f47efe6358c02eea1f9d0ece10b2a4bd"},"schema_version":"1.0","source":{"id":"1205.4219","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.4219","created_at":"2026-05-18T03:04:24Z"},{"alias_kind":"arxiv_version","alias_value":"1205.4219v2","created_at":"2026-05-18T03:04:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.4219","created_at":"2026-05-18T03:04:24Z"},{"alias_kind":"pith_short_12","alias_value":"FOUHQ4KM5Z2U","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_16","alias_value":"FOUHQ4KM5Z2UAHLY","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_8","alias_value":"FOUHQ4KM","created_at":"2026-05-18T12:27:06Z"}],"graph_snapshots":[{"event_id":"sha256:93ee9530007f45b45a5005c055d93cb11158fda3925f646e7bc3f78440c99157","target":"graph","created_at":"2026-05-18T03:04:24Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"This paper considers testing a covariance matrix $\\Sigma$ in the high dimensional setting where the dimension $p$ can be comparable or much larger than the sample size $n$. The problem of testing the hypothesis $H_0:\\Sigma=\\Sigma_0$ for a given covariance matrix $\\Sigma_0$ is studied from a minimax point of view. We first characterize the boundary that separates the testable region from the non-testable region by the Frobenius norm when the ratio between the dimension $p$ over the sample size $n$ is bounded. A test based on a $U$-statistic is introduced and is shown to be rate optimal over thi","authors_text":"T. Tony Cai, Zongming Ma","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2012-05-18T19:06:15Z","title":"Optimal hypothesis testing for high dimensional covariance matrices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.4219","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:7bc74cbb64da93e14aeef24ab46012291894cac2267fb2e46ea68fb4368d5942","target":"record","created_at":"2026-05-18T03:04:24Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"6ac7f23c148f27382a5ba8d3fb9fe283bcc3c4586ac4453681336fea24fec2ac","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2012-05-18T19:06:15Z","title_canon_sha256":"03b42b14ca98a1e01bb805d8923a59e1f47efe6358c02eea1f9d0ece10b2a4bd"},"schema_version":"1.0","source":{"id":"1205.4219","kind":"arxiv","version":2}},"canonical_sha256":"2ba878714cee75401d7847c7f01acdbb2602de8c8e49fcebc1dd85d0181fb444","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2ba878714cee75401d7847c7f01acdbb2602de8c8e49fcebc1dd85d0181fb444","first_computed_at":"2026-05-18T03:04:24.365943Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:04:24.365943Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xEkL2Zvb+brJA/R6ykbb1TEiVC8MEOBIKogmK3wcL17Vf6sWn+PVCX6O8YQaBgtk/4jVfwSLaGVBj9A8DNg+AA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:04:24.366485Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.4219","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7bc74cbb64da93e14aeef24ab46012291894cac2267fb2e46ea68fb4368d5942","sha256:93ee9530007f45b45a5005c055d93cb11158fda3925f646e7bc3f78440c99157"],"state_sha256":"61584545f29d8a4f88877bc9463593abc243f290ee57f3ab4d949339f2c88cf1"}