{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:5ZFXSYMBRW7OOWGZ72F3VFVKWK","short_pith_number":"pith:5ZFXSYMB","canonical_record":{"source":{"id":"1907.06933","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2019-07-16T10:40:58Z","cross_cats_sorted":["stat.ME","stat.TH"],"title_canon_sha256":"29448586dadc27379b3389723713888699610d1b0e15cb7635612851d9385551","abstract_canon_sha256":"18d0e64f8567a9e7f0068331d9e02ca541409f2577ed00e1be2c6525b380face"},"schema_version":"1.0"},"canonical_sha256":"ee4b7961818dbee758d9fe8bba96aab2ad66b163ccb357ce821c54884736c98f","source":{"kind":"arxiv","id":"1907.06933","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.06933","created_at":"2026-05-17T23:40:28Z"},{"alias_kind":"arxiv_version","alias_value":"1907.06933v1","created_at":"2026-05-17T23:40:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.06933","created_at":"2026-05-17T23:40:28Z"},{"alias_kind":"pith_short_12","alias_value":"5ZFXSYMBRW7O","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_16","alias_value":"5ZFXSYMBRW7OOWGZ","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_8","alias_value":"5ZFXSYMB","created_at":"2026-05-18T12:33:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:5ZFXSYMBRW7OOWGZ72F3VFVKWK","target":"record","payload":{"canonical_record":{"source":{"id":"1907.06933","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2019-07-16T10:40:58Z","cross_cats_sorted":["stat.ME","stat.TH"],"title_canon_sha256":"29448586dadc27379b3389723713888699610d1b0e15cb7635612851d9385551","abstract_canon_sha256":"18d0e64f8567a9e7f0068331d9e02ca541409f2577ed00e1be2c6525b380face"},"schema_version":"1.0"},"canonical_sha256":"ee4b7961818dbee758d9fe8bba96aab2ad66b163ccb357ce821c54884736c98f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:40:28.636610Z","signature_b64":"/3h5Usn4yz2WTZOfUTbhlfdJ53ln5pXLRefhe7dbtrzHFaFAlUmh2/PMa/+r0Uuk6rhAez74ElGfDwiO9ZN0DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ee4b7961818dbee758d9fe8bba96aab2ad66b163ccb357ce821c54884736c98f","last_reissued_at":"2026-05-17T23:40:28.636032Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:40:28.636032Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1907.06933","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":"2026-05-17T23:40:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"46P7Bx8SUSKXTHsZdQMc9t4md6ovuT94g+AnqHIawAIytXMEBp1+cDFnVnJDaaGoSKaY+qeMKSgjk3a2BTRoCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T18:23:35.469923Z"},"content_sha256":"c78faa9fecf20191e9a747eab10fec2394fa93f50d9eb35ec2bb0671cbb597a6","schema_version":"1.0","event_id":"sha256:c78faa9fecf20191e9a747eab10fec2394fa93f50d9eb35ec2bb0671cbb597a6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:5ZFXSYMBRW7OOWGZ72F3VFVKWK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the $L_p$-error of the Grenander-type estimator in the Cox model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ME","stat.TH"],"primary_cat":"math.ST","authors_text":"C\\'ecile Durot, Eni Musta","submitted_at":"2019-07-16T10:40:58Z","abstract_excerpt":"We consider the Cox regression model and study the asymptotic global behavior of the Grenander-type estimator for a monotone baseline hazard function. This model is not included in the general setting of Durot (2007). However, we show that a similar central limit theorem holds for $L_p$-error of the Grenander-type estimator. We also propose a test procedure for a Weibull baseline distribution, based on the $L_p$-distance between the Grenander estimator and a parametric estimator of the baseline hazard. Simulation studies are performed to investigate the performance of this test."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.06933","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":"2026-05-17T23:40:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YJ7zqjmJdv9fxr7TtYoUx+31rH8s2wNhOoWZ1hfbE3/laDmMjX0VVuavm+jJGWbjMGhoEnSDw8UWLK7232ucCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T18:23:35.470274Z"},"content_sha256":"8d617eb2548fdb28b4bb7dad224930e9e204cc6a53f4aba6bc2db05179658cd0","schema_version":"1.0","event_id":"sha256:8d617eb2548fdb28b4bb7dad224930e9e204cc6a53f4aba6bc2db05179658cd0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5ZFXSYMBRW7OOWGZ72F3VFVKWK/bundle.json","state_url":"https://pith.science/pith/5ZFXSYMBRW7OOWGZ72F3VFVKWK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5ZFXSYMBRW7OOWGZ72F3VFVKWK/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":"2026-06-24T18:23:35Z","links":{"resolver":"https://pith.science/pith/5ZFXSYMBRW7OOWGZ72F3VFVKWK","bundle":"https://pith.science/pith/5ZFXSYMBRW7OOWGZ72F3VFVKWK/bundle.json","state":"https://pith.science/pith/5ZFXSYMBRW7OOWGZ72F3VFVKWK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5ZFXSYMBRW7OOWGZ72F3VFVKWK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:5ZFXSYMBRW7OOWGZ72F3VFVKWK","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":"18d0e64f8567a9e7f0068331d9e02ca541409f2577ed00e1be2c6525b380face","cross_cats_sorted":["stat.ME","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2019-07-16T10:40:58Z","title_canon_sha256":"29448586dadc27379b3389723713888699610d1b0e15cb7635612851d9385551"},"schema_version":"1.0","source":{"id":"1907.06933","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.06933","created_at":"2026-05-17T23:40:28Z"},{"alias_kind":"arxiv_version","alias_value":"1907.06933v1","created_at":"2026-05-17T23:40:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.06933","created_at":"2026-05-17T23:40:28Z"},{"alias_kind":"pith_short_12","alias_value":"5ZFXSYMBRW7O","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_16","alias_value":"5ZFXSYMBRW7OOWGZ","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_8","alias_value":"5ZFXSYMB","created_at":"2026-05-18T12:33:10Z"}],"graph_snapshots":[{"event_id":"sha256:8d617eb2548fdb28b4bb7dad224930e9e204cc6a53f4aba6bc2db05179658cd0","target":"graph","created_at":"2026-05-17T23:40:28Z","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":"We consider the Cox regression model and study the asymptotic global behavior of the Grenander-type estimator for a monotone baseline hazard function. This model is not included in the general setting of Durot (2007). However, we show that a similar central limit theorem holds for $L_p$-error of the Grenander-type estimator. We also propose a test procedure for a Weibull baseline distribution, based on the $L_p$-distance between the Grenander estimator and a parametric estimator of the baseline hazard. Simulation studies are performed to investigate the performance of this test.","authors_text":"C\\'ecile Durot, Eni Musta","cross_cats":["stat.ME","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2019-07-16T10:40:58Z","title":"On the $L_p$-error of the Grenander-type estimator in the Cox model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.06933","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:c78faa9fecf20191e9a747eab10fec2394fa93f50d9eb35ec2bb0671cbb597a6","target":"record","created_at":"2026-05-17T23:40:28Z","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":"18d0e64f8567a9e7f0068331d9e02ca541409f2577ed00e1be2c6525b380face","cross_cats_sorted":["stat.ME","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2019-07-16T10:40:58Z","title_canon_sha256":"29448586dadc27379b3389723713888699610d1b0e15cb7635612851d9385551"},"schema_version":"1.0","source":{"id":"1907.06933","kind":"arxiv","version":1}},"canonical_sha256":"ee4b7961818dbee758d9fe8bba96aab2ad66b163ccb357ce821c54884736c98f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ee4b7961818dbee758d9fe8bba96aab2ad66b163ccb357ce821c54884736c98f","first_computed_at":"2026-05-17T23:40:28.636032Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:40:28.636032Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/3h5Usn4yz2WTZOfUTbhlfdJ53ln5pXLRefhe7dbtrzHFaFAlUmh2/PMa/+r0Uuk6rhAez74ElGfDwiO9ZN0DA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:40:28.636610Z","signed_message":"canonical_sha256_bytes"},"source_id":"1907.06933","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c78faa9fecf20191e9a747eab10fec2394fa93f50d9eb35ec2bb0671cbb597a6","sha256:8d617eb2548fdb28b4bb7dad224930e9e204cc6a53f4aba6bc2db05179658cd0"],"state_sha256":"2b5981dcc4deb5164b3d5cf8759f232c9990ab45d2f239d1646e7dff7a962067"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/IG9QqYBVpvwVglyTDDZ8UlM4Sn8vYCZmwRn7kgClN5EqQRUsUZdlQ4r7qj5LO9YwOi1fB5JUgm0CkG3PmDFDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T18:23:35.472252Z","bundle_sha256":"418591b7e6f200a40e0f4d4c3a797c71239164d1bdaa0648bc30119a49c89677"}}