{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:X3JQR5EAWMT435TKCHWZUU7N7W","short_pith_number":"pith:X3JQR5EA","canonical_record":{"source":{"id":"1204.2579","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2012-04-11T22:06:55Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"4da01e002963ffc9ab9261f29e2c32cb66a0c09981d3ddbae86d889c9dd54a06","abstract_canon_sha256":"4cf34f400b06495398e7779aa954ae86a04d24c2ceae734e4e43836c4cdce734"},"schema_version":"1.0"},"canonical_sha256":"bed308f480b327cdf66a11ed9a53edfdbce39089a49c782959482a8371f6d205","source":{"kind":"arxiv","id":"1204.2579","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.2579","created_at":"2026-05-18T03:58:03Z"},{"alias_kind":"arxiv_version","alias_value":"1204.2579v1","created_at":"2026-05-18T03:58:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.2579","created_at":"2026-05-18T03:58:03Z"},{"alias_kind":"pith_short_12","alias_value":"X3JQR5EAWMT4","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_16","alias_value":"X3JQR5EAWMT435TK","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_8","alias_value":"X3JQR5EA","created_at":"2026-05-18T12:27:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:X3JQR5EAWMT435TKCHWZUU7N7W","target":"record","payload":{"canonical_record":{"source":{"id":"1204.2579","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2012-04-11T22:06:55Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"4da01e002963ffc9ab9261f29e2c32cb66a0c09981d3ddbae86d889c9dd54a06","abstract_canon_sha256":"4cf34f400b06495398e7779aa954ae86a04d24c2ceae734e4e43836c4cdce734"},"schema_version":"1.0"},"canonical_sha256":"bed308f480b327cdf66a11ed9a53edfdbce39089a49c782959482a8371f6d205","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:58:03.993722Z","signature_b64":"f3jHLZMUDOPc0ugvRqgxqyEFB0X9oJ2GPgWmPGH8UVDy3QNJBQ+8a6JtdQBE7l2P1gcQdRMoaLtihZnt5+rfAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bed308f480b327cdf66a11ed9a53edfdbce39089a49c782959482a8371f6d205","last_reissued_at":"2026-05-18T03:58:03.993083Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:58:03.993083Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1204.2579","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":"2026-05-18T03:58:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hSW+Z5qDwNnZJqtdCmA0uZ2IYaDz/URSgCyMxF9QS8eku+KNKcdh4orkp3/CYAgc1TVd+wOGNJ0LJ8XaFgrWBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T15:23:45.087364Z"},"content_sha256":"835ad949d60d872f67c099a31118ca8cde70ea145a43a06c17c4541a908e5add","schema_version":"1.0","event_id":"sha256:835ad949d60d872f67c099a31118ca8cde70ea145a43a06c17c4541a908e5add"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:X3JQR5EAWMT435TKCHWZUU7N7W","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A general semiparametric Z-estimation approach for case-cohort studies","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Bin Nan, Jon A. Wellner","submitted_at":"2012-04-11T22:06:55Z","abstract_excerpt":"Case-cohort design, an outcome-dependent sampling design for censored survival data, is increasingly used in biomedical research. The development of asymptotic theory for a case-cohort design in the current literature primarily relies on counting process stochastic integrals. Such an approach, however, is rather limited and lacks theoretical justification for outcome-dependent weighted methods due to non-predictability. Instead of stochastic integrals, we derive asymptotic properties for case-cohort studies based on a general Z-estimation theory for semiparametric models with bundled parameter"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.2579","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":"2026-05-18T03:58:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/upOoFPjWf7OuRU5s4KklbyKP0dY7t3FeHVUlywTcfFrNNTlfAG1mYi3aVMbucExDdcr5tN20MVqTnc9SG3UCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T15:23:45.087726Z"},"content_sha256":"4fa4e94f20b498a2fe2f50411560aa9c036a4b5cf8bccb369a80d404d85753ca","schema_version":"1.0","event_id":"sha256:4fa4e94f20b498a2fe2f50411560aa9c036a4b5cf8bccb369a80d404d85753ca"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/X3JQR5EAWMT435TKCHWZUU7N7W/bundle.json","state_url":"https://pith.science/pith/X3JQR5EAWMT435TKCHWZUU7N7W/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/X3JQR5EAWMT435TKCHWZUU7N7W/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":"2026-06-05T15:23:45Z","links":{"resolver":"https://pith.science/pith/X3JQR5EAWMT435TKCHWZUU7N7W","bundle":"https://pith.science/pith/X3JQR5EAWMT435TKCHWZUU7N7W/bundle.json","state":"https://pith.science/pith/X3JQR5EAWMT435TKCHWZUU7N7W/state.json","well_known_bundle":"https://pith.science/.well-known/pith/X3JQR5EAWMT435TKCHWZUU7N7W/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:X3JQR5EAWMT435TKCHWZUU7N7W","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":"4cf34f400b06495398e7779aa954ae86a04d24c2ceae734e4e43836c4cdce734","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2012-04-11T22:06:55Z","title_canon_sha256":"4da01e002963ffc9ab9261f29e2c32cb66a0c09981d3ddbae86d889c9dd54a06"},"schema_version":"1.0","source":{"id":"1204.2579","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.2579","created_at":"2026-05-18T03:58:03Z"},{"alias_kind":"arxiv_version","alias_value":"1204.2579v1","created_at":"2026-05-18T03:58:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.2579","created_at":"2026-05-18T03:58:03Z"},{"alias_kind":"pith_short_12","alias_value":"X3JQR5EAWMT4","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_16","alias_value":"X3JQR5EAWMT435TK","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_8","alias_value":"X3JQR5EA","created_at":"2026-05-18T12:27:27Z"}],"graph_snapshots":[{"event_id":"sha256:4fa4e94f20b498a2fe2f50411560aa9c036a4b5cf8bccb369a80d404d85753ca","target":"graph","created_at":"2026-05-18T03:58:03Z","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":"Case-cohort design, an outcome-dependent sampling design for censored survival data, is increasingly used in biomedical research. The development of asymptotic theory for a case-cohort design in the current literature primarily relies on counting process stochastic integrals. Such an approach, however, is rather limited and lacks theoretical justification for outcome-dependent weighted methods due to non-predictability. Instead of stochastic integrals, we derive asymptotic properties for case-cohort studies based on a general Z-estimation theory for semiparametric models with bundled parameter","authors_text":"Bin Nan, Jon A. Wellner","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2012-04-11T22:06:55Z","title":"A general semiparametric Z-estimation approach for case-cohort studies"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.2579","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":"sha256:835ad949d60d872f67c099a31118ca8cde70ea145a43a06c17c4541a908e5add","target":"record","created_at":"2026-05-18T03:58:03Z","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":"4cf34f400b06495398e7779aa954ae86a04d24c2ceae734e4e43836c4cdce734","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2012-04-11T22:06:55Z","title_canon_sha256":"4da01e002963ffc9ab9261f29e2c32cb66a0c09981d3ddbae86d889c9dd54a06"},"schema_version":"1.0","source":{"id":"1204.2579","kind":"arxiv","version":1}},"canonical_sha256":"bed308f480b327cdf66a11ed9a53edfdbce39089a49c782959482a8371f6d205","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bed308f480b327cdf66a11ed9a53edfdbce39089a49c782959482a8371f6d205","first_computed_at":"2026-05-18T03:58:03.993083Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:58:03.993083Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"f3jHLZMUDOPc0ugvRqgxqyEFB0X9oJ2GPgWmPGH8UVDy3QNJBQ+8a6JtdQBE7l2P1gcQdRMoaLtihZnt5+rfAw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:58:03.993722Z","signed_message":"canonical_sha256_bytes"},"source_id":"1204.2579","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:835ad949d60d872f67c099a31118ca8cde70ea145a43a06c17c4541a908e5add","sha256:4fa4e94f20b498a2fe2f50411560aa9c036a4b5cf8bccb369a80d404d85753ca"],"state_sha256":"a6570866ae32102af13d61b7ebd1eaff202fab74ea026a6879f79bcb6f3e6e21"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9YaTfnd8XaTlQt4PcV67idiDBE38F26vL8KCEmXiU34KjkHfZd+Uk+xdINTDBcCbZ9BDH1k7ojW3yNcIGzwJCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T15:23:45.089936Z","bundle_sha256":"1c1e5ede916568cc9895be8456a7aacd5cc189cd65a8af747a160ebc9b88bb67"}}