{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:BY4WGQTGNGWYE5IXSZU32JWIQN","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":"a1d94ecb002a2d1c219ffeab4439368068f5e4ce5a991f54a4e392dc4e04871d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2015-08-11T07:20:25Z","title_canon_sha256":"0ea482e675f6649334ad59b3d75ee55f25e67e32a53082f248483a5288240d6e"},"schema_version":"1.0","source":{"id":"1508.02498","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.02498","created_at":"2026-05-18T01:19:40Z"},{"alias_kind":"arxiv_version","alias_value":"1508.02498v3","created_at":"2026-05-18T01:19:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.02498","created_at":"2026-05-18T01:19:40Z"},{"alias_kind":"pith_short_12","alias_value":"BY4WGQTGNGWY","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_16","alias_value":"BY4WGQTGNGWYE5IX","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_8","alias_value":"BY4WGQTG","created_at":"2026-05-18T12:29:14Z"}],"graph_snapshots":[{"event_id":"sha256:8a196f5857c2d84b585616eba49c85b8436935d34baec399ebef32e6aeec778b","target":"graph","created_at":"2026-05-18T01:19:40Z","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 focuses on the prominent sphericity test when the dimension $p$ is much lager than sample size $n$. The classical likelihood ratio test(LRT) is no longer applicable when $p\\gg n$. Therefore a Quasi-LRT is proposed and asymptotic distribution of the test statistic under the null when $p/n\\rightarrow\\infty, n\\rightarrow\\infty$ is well established in this paper. Meanwhile, John's test has been found to possess the powerful {\\it dimension-proof} property, which keeps exactly the same limiting distribution under the null with any $(n,p)$-asymptotic, i.e. $p/n\\rightarrow[0,\\infty]$, $n\\ri","authors_text":"Jianfeng Yao, Zeng Li","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2015-08-11T07:20:25Z","title":"Testing the Sphericity of a covariance matrix when the dimension is much larger than the sample size"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.02498","kind":"arxiv","version":3},"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":"sha256:71245253f33a734a24e209115422e23a716c3b69e56333e25ecec7e4faa0e348","target":"record","created_at":"2026-05-18T01:19:40Z","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":"a1d94ecb002a2d1c219ffeab4439368068f5e4ce5a991f54a4e392dc4e04871d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2015-08-11T07:20:25Z","title_canon_sha256":"0ea482e675f6649334ad59b3d75ee55f25e67e32a53082f248483a5288240d6e"},"schema_version":"1.0","source":{"id":"1508.02498","kind":"arxiv","version":3}},"canonical_sha256":"0e3963426669ad8275179669bd26c88346256f2c2431d36f03cc497cf7ad6449","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0e3963426669ad8275179669bd26c88346256f2c2431d36f03cc497cf7ad6449","first_computed_at":"2026-05-18T01:19:40.714878Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:19:40.714878Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wcfNagrh2HiwN0gqZPKlgQD8bA3FiSlzpR44blpmsARVLwSvUmbC+Z4744Zs00kHtIfiarVry0hbMKjalNKJBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:19:40.715518Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.02498","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:71245253f33a734a24e209115422e23a716c3b69e56333e25ecec7e4faa0e348","sha256:8a196f5857c2d84b585616eba49c85b8436935d34baec399ebef32e6aeec778b"],"state_sha256":"55b9342ed25b9189c6a79c58cb8d8c5a0b9f63bfda60dc15e4c50b4756af1a7c"}