{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:QBETJHNAAJI67KWS62GXGCQUFW","short_pith_number":"pith:QBETJHNA","canonical_record":{"source":{"id":"1304.2180","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2013-04-08T12:23:36Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"53526d136f236563aedbf5e9aebb899024178b240c464563801383fbef6aa9b2","abstract_canon_sha256":"c9af1d90154e3ff6bb9a97e993c6a854c32ffd560917faa66dc0a45ebbf1c621"},"schema_version":"1.0"},"canonical_sha256":"8049349da00251efaad2f68d730a142db9c23470119c5e81a010ea1d17e25fe8","source":{"kind":"arxiv","id":"1304.2180","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.2180","created_at":"2026-05-18T03:28:43Z"},{"alias_kind":"arxiv_version","alias_value":"1304.2180v1","created_at":"2026-05-18T03:28:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.2180","created_at":"2026-05-18T03:28:43Z"},{"alias_kind":"pith_short_12","alias_value":"QBETJHNAAJI6","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"QBETJHNAAJI67KWS","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"QBETJHNA","created_at":"2026-05-18T12:27:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:QBETJHNAAJI67KWS62GXGCQUFW","target":"record","payload":{"canonical_record":{"source":{"id":"1304.2180","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2013-04-08T12:23:36Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"53526d136f236563aedbf5e9aebb899024178b240c464563801383fbef6aa9b2","abstract_canon_sha256":"c9af1d90154e3ff6bb9a97e993c6a854c32ffd560917faa66dc0a45ebbf1c621"},"schema_version":"1.0"},"canonical_sha256":"8049349da00251efaad2f68d730a142db9c23470119c5e81a010ea1d17e25fe8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:28:43.761518Z","signature_b64":"OIE2qJ5TvFtiUHzZx1ulel3GPMfObl5eda5Ecdm+f1WBaA9cLzfjjEiH4t3t4ji6VV6ri6HjzMztz5B08PIKBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8049349da00251efaad2f68d730a142db9c23470119c5e81a010ea1d17e25fe8","last_reissued_at":"2026-05-18T03:28:43.760792Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:28:43.760792Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1304.2180","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:28:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IXgPdPv3PfGs5Sta9J5ESP/pPUpc57Dt+6E4XDVMf/T2fNVwsfPeVDQDd9lvR7QYIKwXxifdNd0egIw20jgUCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T21:59:32.754623Z"},"content_sha256":"ffb8cd323da470ca8b8d4e9ae9af0f140400bc28855cd7c252f2b1d128dc8143","schema_version":"1.0","event_id":"sha256:ffb8cd323da470ca8b8d4e9ae9af0f140400bc28855cd7c252f2b1d128dc8143"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:QBETJHNAAJI67KWS62GXGCQUFW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Cram\\'{e}r moderate deviation theorem for Hotelling's $T^2$-statistic with applications to global tests","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Qi-Man Shao, Weidong Liu","submitted_at":"2013-04-08T12:23:36Z","abstract_excerpt":"A Cramer moderate deviation theorem for Hotelling's $T^2$-statistic is proved under a finite $(3+\\delta)$th moment. The result is applied to large scale tests on the equality of mean vectors and is shown that the number of tests can be as large as $e^{o(n^{1/3})}$ before the chi-squared distribution calibration becomes inaccurate. As an application of the moderate deviation results, a global test on the equality of m mean vectors based on the maximum of Hotelling's $T^2$-statistics is developed and its asymptotic null distribution is shown to be an extreme value type I distribution. A novel in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.2180","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:28:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sjVkCC+x7Pl6QDus/Pwr9IwVDBI8qDROLjBFu2zm4q1r1gnSw0kg9Iq5mULIWrscRht+bEHmeG3LkdbpngiXBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T21:59:32.755304Z"},"content_sha256":"f29eb53e91f65b99e8f3e2a73b31d397960bf1ffdf9ea395e8120527c326eb0a","schema_version":"1.0","event_id":"sha256:f29eb53e91f65b99e8f3e2a73b31d397960bf1ffdf9ea395e8120527c326eb0a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QBETJHNAAJI67KWS62GXGCQUFW/bundle.json","state_url":"https://pith.science/pith/QBETJHNAAJI67KWS62GXGCQUFW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QBETJHNAAJI67KWS62GXGCQUFW/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-26T21:59:32Z","links":{"resolver":"https://pith.science/pith/QBETJHNAAJI67KWS62GXGCQUFW","bundle":"https://pith.science/pith/QBETJHNAAJI67KWS62GXGCQUFW/bundle.json","state":"https://pith.science/pith/QBETJHNAAJI67KWS62GXGCQUFW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QBETJHNAAJI67KWS62GXGCQUFW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:QBETJHNAAJI67KWS62GXGCQUFW","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":"c9af1d90154e3ff6bb9a97e993c6a854c32ffd560917faa66dc0a45ebbf1c621","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2013-04-08T12:23:36Z","title_canon_sha256":"53526d136f236563aedbf5e9aebb899024178b240c464563801383fbef6aa9b2"},"schema_version":"1.0","source":{"id":"1304.2180","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.2180","created_at":"2026-05-18T03:28:43Z"},{"alias_kind":"arxiv_version","alias_value":"1304.2180v1","created_at":"2026-05-18T03:28:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.2180","created_at":"2026-05-18T03:28:43Z"},{"alias_kind":"pith_short_12","alias_value":"QBETJHNAAJI6","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"QBETJHNAAJI67KWS","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"QBETJHNA","created_at":"2026-05-18T12:27:57Z"}],"graph_snapshots":[{"event_id":"sha256:f29eb53e91f65b99e8f3e2a73b31d397960bf1ffdf9ea395e8120527c326eb0a","target":"graph","created_at":"2026-05-18T03:28:43Z","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":"A Cramer moderate deviation theorem for Hotelling's $T^2$-statistic is proved under a finite $(3+\\delta)$th moment. The result is applied to large scale tests on the equality of mean vectors and is shown that the number of tests can be as large as $e^{o(n^{1/3})}$ before the chi-squared distribution calibration becomes inaccurate. As an application of the moderate deviation results, a global test on the equality of m mean vectors based on the maximum of Hotelling's $T^2$-statistics is developed and its asymptotic null distribution is shown to be an extreme value type I distribution. A novel in","authors_text":"Qi-Man Shao, Weidong Liu","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2013-04-08T12:23:36Z","title":"A Cram\\'{e}r moderate deviation theorem for Hotelling's $T^2$-statistic with applications to global tests"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.2180","kind":"arxiv","version":1},"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:ffb8cd323da470ca8b8d4e9ae9af0f140400bc28855cd7c252f2b1d128dc8143","target":"record","created_at":"2026-05-18T03:28:43Z","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":"c9af1d90154e3ff6bb9a97e993c6a854c32ffd560917faa66dc0a45ebbf1c621","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2013-04-08T12:23:36Z","title_canon_sha256":"53526d136f236563aedbf5e9aebb899024178b240c464563801383fbef6aa9b2"},"schema_version":"1.0","source":{"id":"1304.2180","kind":"arxiv","version":1}},"canonical_sha256":"8049349da00251efaad2f68d730a142db9c23470119c5e81a010ea1d17e25fe8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8049349da00251efaad2f68d730a142db9c23470119c5e81a010ea1d17e25fe8","first_computed_at":"2026-05-18T03:28:43.760792Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:28:43.760792Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OIE2qJ5TvFtiUHzZx1ulel3GPMfObl5eda5Ecdm+f1WBaA9cLzfjjEiH4t3t4ji6VV6ri6HjzMztz5B08PIKBA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:28:43.761518Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.2180","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ffb8cd323da470ca8b8d4e9ae9af0f140400bc28855cd7c252f2b1d128dc8143","sha256:f29eb53e91f65b99e8f3e2a73b31d397960bf1ffdf9ea395e8120527c326eb0a"],"state_sha256":"6a1d6aa1a5dd9086fd619c1c5344ad8724c5a7d1f9e7e4bfef813d711c2c0a04"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ia9DhJxjjsTJapGmySvHNAFjs6kS7xrUKAkuB9vJkZNq8Y/GmZcIFTPD7RG/rNiLC6a1/ADNsaNOn29g86i8DQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T21:59:32.757978Z","bundle_sha256":"c5e15ba8c485eb9821707eb03615c6159edf782ebd1bac0adc7046ba2faf3daa"}}