{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:PQQ2Z6E7FTMTTFANOCBSZCADDM","short_pith_number":"pith:PQQ2Z6E7","schema_version":"1.0","canonical_sha256":"7c21acf89f2cd939940d70832c88031b09bb355537de3928bc24d11ed1939c3a","source":{"kind":"arxiv","id":"1611.01506","version":2},"attestation_state":"computed","paper":{"title":"Isotonized smooth estimators of a monotone baseline hazard in the Cox model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Eni Musta, Hendrik P. Lopuha\\\"a","submitted_at":"2016-11-04T19:42:48Z","abstract_excerpt":"We consider two isotonic smooth estimators for a monotone baseline hazard in the Cox model, a maximum smooth likelihood estimator and a Grenander-type estimator based on the smoothed Breslow estimator for the cumulative baseline hazard. We show that they are both asymptotically normal at rate $n^{m/(2m+1)}$, where $m\\geq 2$ denotes the level of smoothness considered, and we relate their limit behavior to kernel smoothed isotonic estimators studied in Lopuha\\\"a and Musta (2016). It turns out that the Grenander-type estimator is asymptotically equivalent to the kernel smoothed isotonic estimator"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1611.01506","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2016-11-04T19:42:48Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"29d87d72b8d8511729980723c84f3ffdbb824c9287bca53ab7a22910965aa397","abstract_canon_sha256":"4109bd32d965a39bfaf47232bcb47155923c58c50a5ad45a13d69a9ce5ac3e2c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:15:47.452388Z","signature_b64":"aAnScoSW5RPegmdKuAlSU+PvrDHcQAXZ/XLwSYfC0Tl4ew8cCruj1Qb1V74XwlYffoMwoy/BUkysVgJK3KC5CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7c21acf89f2cd939940d70832c88031b09bb355537de3928bc24d11ed1939c3a","last_reissued_at":"2026-05-18T00:15:47.451713Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:15:47.451713Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Isotonized smooth estimators of a monotone baseline hazard in the Cox model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Eni Musta, Hendrik P. Lopuha\\\"a","submitted_at":"2016-11-04T19:42:48Z","abstract_excerpt":"We consider two isotonic smooth estimators for a monotone baseline hazard in the Cox model, a maximum smooth likelihood estimator and a Grenander-type estimator based on the smoothed Breslow estimator for the cumulative baseline hazard. We show that they are both asymptotically normal at rate $n^{m/(2m+1)}$, where $m\\geq 2$ denotes the level of smoothness considered, and we relate their limit behavior to kernel smoothed isotonic estimators studied in Lopuha\\\"a and Musta (2016). It turns out that the Grenander-type estimator is asymptotically equivalent to the kernel smoothed isotonic estimator"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.01506","kind":"arxiv","version":2},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1611.01506","created_at":"2026-05-18T00:15:47.451822+00:00"},{"alias_kind":"arxiv_version","alias_value":"1611.01506v2","created_at":"2026-05-18T00:15:47.451822+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.01506","created_at":"2026-05-18T00:15:47.451822+00:00"},{"alias_kind":"pith_short_12","alias_value":"PQQ2Z6E7FTMT","created_at":"2026-05-18T12:30:39.010887+00:00"},{"alias_kind":"pith_short_16","alias_value":"PQQ2Z6E7FTMTTFAN","created_at":"2026-05-18T12:30:39.010887+00:00"},{"alias_kind":"pith_short_8","alias_value":"PQQ2Z6E7","created_at":"2026-05-18T12:30:39.010887+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/PQQ2Z6E7FTMTTFANOCBSZCADDM","json":"https://pith.science/pith/PQQ2Z6E7FTMTTFANOCBSZCADDM.json","graph_json":"https://pith.science/api/pith-number/PQQ2Z6E7FTMTTFANOCBSZCADDM/graph.json","events_json":"https://pith.science/api/pith-number/PQQ2Z6E7FTMTTFANOCBSZCADDM/events.json","paper":"https://pith.science/paper/PQQ2Z6E7"},"agent_actions":{"view_html":"https://pith.science/pith/PQQ2Z6E7FTMTTFANOCBSZCADDM","download_json":"https://pith.science/pith/PQQ2Z6E7FTMTTFANOCBSZCADDM.json","view_paper":"https://pith.science/paper/PQQ2Z6E7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1611.01506&json=true","fetch_graph":"https://pith.science/api/pith-number/PQQ2Z6E7FTMTTFANOCBSZCADDM/graph.json","fetch_events":"https://pith.science/api/pith-number/PQQ2Z6E7FTMTTFANOCBSZCADDM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PQQ2Z6E7FTMTTFANOCBSZCADDM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PQQ2Z6E7FTMTTFANOCBSZCADDM/action/storage_attestation","attest_author":"https://pith.science/pith/PQQ2Z6E7FTMTTFANOCBSZCADDM/action/author_attestation","sign_citation":"https://pith.science/pith/PQQ2Z6E7FTMTTFANOCBSZCADDM/action/citation_signature","submit_replication":"https://pith.science/pith/PQQ2Z6E7FTMTTFANOCBSZCADDM/action/replication_record"}},"created_at":"2026-05-18T00:15:47.451822+00:00","updated_at":"2026-05-18T00:15:47.451822+00:00"}