{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:PGG6JVQA6FIIB6UKYP2KBPKAWM","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":"57e58bee891cd5401ddd3811e00d86469cb6312bd79f7190dcb3a02efe7a143a","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2017-08-09T14:28:47Z","title_canon_sha256":"b5bc3a2aa5250dbcec5570bca0942d694fa94d342e86a2654176081e31aa6566"},"schema_version":"1.0","source":{"id":"1708.02854","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.02854","created_at":"2026-05-17T23:54:16Z"},{"alias_kind":"arxiv_version","alias_value":"1708.02854v2","created_at":"2026-05-17T23:54:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.02854","created_at":"2026-05-17T23:54:16Z"},{"alias_kind":"pith_short_12","alias_value":"PGG6JVQA6FII","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_16","alias_value":"PGG6JVQA6FIIB6UK","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_8","alias_value":"PGG6JVQA","created_at":"2026-05-18T12:31:37Z"}],"graph_snapshots":[{"event_id":"sha256:6726f1d6ace3e14aceadd21d754842b8ae1e3ee55158a1c41c2e6ac56212e708","target":"graph","created_at":"2026-05-17T23:54:16Z","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":"Consider a Poisson point process with unknown support boundary curve $g$, which forms a prototype of an irregular statistical model. We address the problem of estimating non-linear functionals of the form $\\int \\Phi(g(x))\\,dx$. Following a nonparametric maximum-likelihood approach, we construct an estimator which is UMVU over H\\\"older balls and achieves the (local) minimax rate of convergence. These results hold under weak assumptions on $\\Phi$ which are satisfied for $\\Phi(u)=|u|^p$, $p\\ge 1$. As an application, we consider the problem of estimating the $L^p$-norm and derive the minimax separ","authors_text":"Markus Rei\\ss, Martin Wahl","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2017-08-09T14:28:47Z","title":"Functional estimation and hypothesis testing in nonparametric boundary models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.02854","kind":"arxiv","version":2},"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":"sha256:49e3c4971f339d89037b17792ec109a530da89d92ce1fefbdb619d740d3dc670","target":"record","created_at":"2026-05-17T23:54:16Z","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":"57e58bee891cd5401ddd3811e00d86469cb6312bd79f7190dcb3a02efe7a143a","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2017-08-09T14:28:47Z","title_canon_sha256":"b5bc3a2aa5250dbcec5570bca0942d694fa94d342e86a2654176081e31aa6566"},"schema_version":"1.0","source":{"id":"1708.02854","kind":"arxiv","version":2}},"canonical_sha256":"798de4d600f15080fa8ac3f4a0bd40b334ccfbcd508a163996b3e5f82981ea14","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"798de4d600f15080fa8ac3f4a0bd40b334ccfbcd508a163996b3e5f82981ea14","first_computed_at":"2026-05-17T23:54:16.924731Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:54:16.924731Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"krKX6iLdzrKPf1byY7x7GN0D9HuyaPSA2QKOBtykVuFQuNjclsittaFJdfnQQ/0TBW3WwIObc+4kMmeW4o2ZBQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:54:16.925247Z","signed_message":"canonical_sha256_bytes"},"source_id":"1708.02854","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:49e3c4971f339d89037b17792ec109a530da89d92ce1fefbdb619d740d3dc670","sha256:6726f1d6ace3e14aceadd21d754842b8ae1e3ee55158a1c41c2e6ac56212e708"],"state_sha256":"6aee4aa61bbdbabde3ce3a86ed065b73f739048fa8a8a2285595d89ffa78b4e4"}