{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:MEAFSD4PCR7WSLXBU6ONGJ63J3","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":"76e9630e1705bc62736e203e8eed48d18a31ca6de40855a6431e7e3770360fd7","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2015-02-19T09:33:44Z","title_canon_sha256":"66e877c348f31991e28d70a82ae56c0186a89e0024de660a12a0d2566eacac26"},"schema_version":"1.0","source":{"id":"1502.05510","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.05510","created_at":"2026-05-18T01:22:14Z"},{"alias_kind":"arxiv_version","alias_value":"1502.05510v3","created_at":"2026-05-18T01:22:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.05510","created_at":"2026-05-18T01:22:14Z"},{"alias_kind":"pith_short_12","alias_value":"MEAFSD4PCR7W","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"MEAFSD4PCR7WSLXB","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"MEAFSD4P","created_at":"2026-05-18T12:29:32Z"}],"graph_snapshots":[{"event_id":"sha256:9e700d167b2296f3ad87c0fbac6203d2eaa286c258dd2a51c304f64f9ad8f003","target":"graph","created_at":"2026-05-18T01:22:14Z","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":"Based on observations of points uniformly distributed over a convex set in $\\R^d$, a new estimator for the volume of the convex set is proposed. The estimator is minimax optimal and also efficient non-asymptotically: it is nearly unbiased with minimal variance among all unbiased oracle-type estimators. Our approach is based on a Poisson point process model and as an ingredient, we prove that the convex hull is a sufficient and complete statistic. No hypotheses on the boundary of the convex set are imposed. In a numerical study, we show that the estimator outperforms earlier estimators for the ","authors_text":"Markus Rei{\\ss}, Nikolay Baldin","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2015-02-19T09:33:44Z","title":"Unbiased estimation of the volume of a convex body"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.05510","kind":"arxiv","version":3},"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":"sha256:4c5ae6bc780f3cb0c56d6068ab4c05a2c28a3f80463d31261432fd5626c065e3","target":"record","created_at":"2026-05-18T01:22:14Z","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":"76e9630e1705bc62736e203e8eed48d18a31ca6de40855a6431e7e3770360fd7","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2015-02-19T09:33:44Z","title_canon_sha256":"66e877c348f31991e28d70a82ae56c0186a89e0024de660a12a0d2566eacac26"},"schema_version":"1.0","source":{"id":"1502.05510","kind":"arxiv","version":3}},"canonical_sha256":"6100590f8f147f692ee1a79cd327db4ecd48a9114eb9fa67a6615d324e44eb71","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6100590f8f147f692ee1a79cd327db4ecd48a9114eb9fa67a6615d324e44eb71","first_computed_at":"2026-05-18T01:22:14.664669Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:22:14.664669Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"A5fVnQHKbDzBUDLZiNzMm5mLu5AZt/4TuPVheJydvQvgEk6wa3Pbzvwi3Z0M04VNmMuC74YZ0zDCld4dChCWDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:22:14.665401Z","signed_message":"canonical_sha256_bytes"},"source_id":"1502.05510","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4c5ae6bc780f3cb0c56d6068ab4c05a2c28a3f80463d31261432fd5626c065e3","sha256:9e700d167b2296f3ad87c0fbac6203d2eaa286c258dd2a51c304f64f9ad8f003"],"state_sha256":"3df0f1277411191a2fe136db00077ba4f81e848101139718bb9a72a363cff73c"}