{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:6ASQJAV4D2M3SYP4E3E3RW2JWM","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":"132871f25f7bc027fceed701233ffe52b314be88704da3146419ed845a2dd924","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2015-07-06T15:21:44Z","title_canon_sha256":"b53b9305ad677d9e8d4c36bc91644c5b34216e77f63943223b12cd52ece06b60"},"schema_version":"1.0","source":{"id":"1507.01494","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.01494","created_at":"2026-05-18T01:37:16Z"},{"alias_kind":"arxiv_version","alias_value":"1507.01494v1","created_at":"2026-05-18T01:37:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.01494","created_at":"2026-05-18T01:37:16Z"},{"alias_kind":"pith_short_12","alias_value":"6ASQJAV4D2M3","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_16","alias_value":"6ASQJAV4D2M3SYP4","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_8","alias_value":"6ASQJAV4","created_at":"2026-05-18T12:29:07Z"}],"graph_snapshots":[{"event_id":"sha256:79bce74a171350cc70b8cc7edd41c1482e50af9fb4e286b8a839534d59f4afcf","target":"graph","created_at":"2026-05-18T01:37:16Z","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 investigate the problems of drift estimation for a shifted Brownian motion and intensity estimation for a Cox process on a finite interval $[0,T]$, when the risk is given by the energy functional associated to some fractional Sobolev space $H^1_0\\subset W^{\\alpha,2}\\subset L^2$. In both situations, Cramer-Rao lower bounds are obtained, entailing in particular that no unbiased estimators with finite risk in $H^1_0$ exist. By Malliavin calculus techniques, we also study super-efficient Stein type estimators (in the Gaussian case).","authors_text":"Dario Trevisan, Eni Musta, Maurizio Pratelli","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2015-07-06T15:21:44Z","title":"Functional Cramer-Rao bounds and Stein estimators in Sobolev spaces, for Brownian motion and Cox processes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.01494","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":"sha256:0088ee8e344ca8d92d807b523805b999112f0be376e4f182dc86bbdd4362b189","target":"record","created_at":"2026-05-18T01:37:16Z","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":"132871f25f7bc027fceed701233ffe52b314be88704da3146419ed845a2dd924","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2015-07-06T15:21:44Z","title_canon_sha256":"b53b9305ad677d9e8d4c36bc91644c5b34216e77f63943223b12cd52ece06b60"},"schema_version":"1.0","source":{"id":"1507.01494","kind":"arxiv","version":1}},"canonical_sha256":"f0250482bc1e99b961fc26c9b8db49b31606e54de4b95c290814113d80467dfb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f0250482bc1e99b961fc26c9b8db49b31606e54de4b95c290814113d80467dfb","first_computed_at":"2026-05-18T01:37:16.785733Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:37:16.785733Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hq5tBf57mMy9emdIfvPYPXk5Z7fmhU0PQieq14JFI5Vyf1vt/cXrceTncJ5DVS+ck8SjrqfFpF/PYqqSbv2VDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:37:16.786297Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.01494","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0088ee8e344ca8d92d807b523805b999112f0be376e4f182dc86bbdd4362b189","sha256:79bce74a171350cc70b8cc7edd41c1482e50af9fb4e286b8a839534d59f4afcf"],"state_sha256":"d9262cf1fc9ec7422f0b6dfc2988a15633dd678eba217ca2ac0350e871bc1ca7"}