{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:L5FGRPMZ4JTT2B77H3IVMCTU5Q","short_pith_number":"pith:L5FGRPMZ","canonical_record":{"source":{"id":"1310.8123","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2013-10-30T12:42:05Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"3e6f6f6f46a1dd9406f6a4802c8a23a909fc5baf3c14dfa6087fe007c9bfb121","abstract_canon_sha256":"df370205df669128140a299b6171ac65af40346258188a421631d8c36804a4ed"},"schema_version":"1.0"},"canonical_sha256":"5f4a68bd99e2673d07ff3ed1560a74ec112f400d00022d2b827987362bea49c4","source":{"kind":"arxiv","id":"1310.8123","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.8123","created_at":"2026-05-18T03:08:25Z"},{"alias_kind":"arxiv_version","alias_value":"1310.8123v1","created_at":"2026-05-18T03:08:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.8123","created_at":"2026-05-18T03:08:25Z"},{"alias_kind":"pith_short_12","alias_value":"L5FGRPMZ4JTT","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_16","alias_value":"L5FGRPMZ4JTT2B77","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_8","alias_value":"L5FGRPMZ","created_at":"2026-05-18T12:27:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:L5FGRPMZ4JTT2B77H3IVMCTU5Q","target":"record","payload":{"canonical_record":{"source":{"id":"1310.8123","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2013-10-30T12:42:05Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"3e6f6f6f46a1dd9406f6a4802c8a23a909fc5baf3c14dfa6087fe007c9bfb121","abstract_canon_sha256":"df370205df669128140a299b6171ac65af40346258188a421631d8c36804a4ed"},"schema_version":"1.0"},"canonical_sha256":"5f4a68bd99e2673d07ff3ed1560a74ec112f400d00022d2b827987362bea49c4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:08:25.918053Z","signature_b64":"ays40mWSbUa1GKZBJudcj2zER14nFkqeejppC+gLtBNstBH+58g6xq/mxYjGL1bKCwUgqS8IzX3BtLZ8G7tHDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5f4a68bd99e2673d07ff3ed1560a74ec112f400d00022d2b827987362bea49c4","last_reissued_at":"2026-05-18T03:08:25.917364Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:08:25.917364Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1310.8123","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":"2026-05-18T03:08:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"21JrDILjKf5hhLJruTipgRL5abChWjcfO/NZSBNlfq4+GSt56BoHhuaN1XBbOUdoX83P8ZHO+Howv/Aq4ijpDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T23:02:43.345611Z"},"content_sha256":"535007e195450d47cc88e2808f952c812e056596ac345eb1cbb96d7d32d34dd6","schema_version":"1.0","event_id":"sha256:535007e195450d47cc88e2808f952c812e056596ac345eb1cbb96d7d32d34dd6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:L5FGRPMZ4JTT2B77H3IVMCTU5Q","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Tests for covariance matrix with fixed or divergent dimension","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Liang Peng, Rongmao Zhang, Ruodu Wang","submitted_at":"2013-10-30T12:42:05Z","abstract_excerpt":"Testing covariance structure is of importance in many areas of statistical analysis, such as microarray analysis and signal processing. Conventional tests for finite-dimensional covariance cannot be applied to high-dimensional data in general, and tests for high-dimensional covariance in the literature usually depend on some special structure of the matrix. In this paper, we propose some empirical likelihood ratio tests for testing whether a covariance matrix equals a given one or has a banded structure. The asymptotic distributions of the new tests are independent of the dimension."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.8123","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":"2026-05-18T03:08:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"s4JEkylKk+JxCNhvcIsRAx2/5KP7yVsjrpoy8IynIWAMhATMdNAKeDkQ/2WVKp7SZx75F5aiMFUqpsINkCvTBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T23:02:43.345960Z"},"content_sha256":"823d5d5447199954a9c897ef579926d15f8fa1acb688888227c5ac09674a1e53","schema_version":"1.0","event_id":"sha256:823d5d5447199954a9c897ef579926d15f8fa1acb688888227c5ac09674a1e53"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/L5FGRPMZ4JTT2B77H3IVMCTU5Q/bundle.json","state_url":"https://pith.science/pith/L5FGRPMZ4JTT2B77H3IVMCTU5Q/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/L5FGRPMZ4JTT2B77H3IVMCTU5Q/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":"2026-06-02T23:02:43Z","links":{"resolver":"https://pith.science/pith/L5FGRPMZ4JTT2B77H3IVMCTU5Q","bundle":"https://pith.science/pith/L5FGRPMZ4JTT2B77H3IVMCTU5Q/bundle.json","state":"https://pith.science/pith/L5FGRPMZ4JTT2B77H3IVMCTU5Q/state.json","well_known_bundle":"https://pith.science/.well-known/pith/L5FGRPMZ4JTT2B77H3IVMCTU5Q/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:L5FGRPMZ4JTT2B77H3IVMCTU5Q","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":"df370205df669128140a299b6171ac65af40346258188a421631d8c36804a4ed","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2013-10-30T12:42:05Z","title_canon_sha256":"3e6f6f6f46a1dd9406f6a4802c8a23a909fc5baf3c14dfa6087fe007c9bfb121"},"schema_version":"1.0","source":{"id":"1310.8123","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.8123","created_at":"2026-05-18T03:08:25Z"},{"alias_kind":"arxiv_version","alias_value":"1310.8123v1","created_at":"2026-05-18T03:08:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.8123","created_at":"2026-05-18T03:08:25Z"},{"alias_kind":"pith_short_12","alias_value":"L5FGRPMZ4JTT","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_16","alias_value":"L5FGRPMZ4JTT2B77","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_8","alias_value":"L5FGRPMZ","created_at":"2026-05-18T12:27:51Z"}],"graph_snapshots":[{"event_id":"sha256:823d5d5447199954a9c897ef579926d15f8fa1acb688888227c5ac09674a1e53","target":"graph","created_at":"2026-05-18T03:08:25Z","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":"Testing covariance structure is of importance in many areas of statistical analysis, such as microarray analysis and signal processing. Conventional tests for finite-dimensional covariance cannot be applied to high-dimensional data in general, and tests for high-dimensional covariance in the literature usually depend on some special structure of the matrix. In this paper, we propose some empirical likelihood ratio tests for testing whether a covariance matrix equals a given one or has a banded structure. The asymptotic distributions of the new tests are independent of the dimension.","authors_text":"Liang Peng, Rongmao Zhang, Ruodu Wang","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2013-10-30T12:42:05Z","title":"Tests for covariance matrix with fixed or divergent dimension"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.8123","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":"sha256:535007e195450d47cc88e2808f952c812e056596ac345eb1cbb96d7d32d34dd6","target":"record","created_at":"2026-05-18T03:08:25Z","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":"df370205df669128140a299b6171ac65af40346258188a421631d8c36804a4ed","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2013-10-30T12:42:05Z","title_canon_sha256":"3e6f6f6f46a1dd9406f6a4802c8a23a909fc5baf3c14dfa6087fe007c9bfb121"},"schema_version":"1.0","source":{"id":"1310.8123","kind":"arxiv","version":1}},"canonical_sha256":"5f4a68bd99e2673d07ff3ed1560a74ec112f400d00022d2b827987362bea49c4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5f4a68bd99e2673d07ff3ed1560a74ec112f400d00022d2b827987362bea49c4","first_computed_at":"2026-05-18T03:08:25.917364Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:08:25.917364Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ays40mWSbUa1GKZBJudcj2zER14nFkqeejppC+gLtBNstBH+58g6xq/mxYjGL1bKCwUgqS8IzX3BtLZ8G7tHDw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:08:25.918053Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.8123","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:535007e195450d47cc88e2808f952c812e056596ac345eb1cbb96d7d32d34dd6","sha256:823d5d5447199954a9c897ef579926d15f8fa1acb688888227c5ac09674a1e53"],"state_sha256":"2d09e5781d4592331199f7b234f955a9135c757db8891937827ad95e47e82528"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"x9/Cux6UbeandL2XBe6IvofVr5NhQ3Ti7BIkhE4RQx8+T/BzKLjuMWSS9WGsOzvj5rWtvotEYEAtMjnrGOoGAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T23:02:43.348027Z","bundle_sha256":"0db3b6138b20538db5816736d3d61ed3ef16ef4b8b06546a5a560052b6c0d4e3"}}