{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:NFXP4NAU5KHN6HAGCONL3LRQPK","short_pith_number":"pith:NFXP4NAU","schema_version":"1.0","canonical_sha256":"696efe3414ea8edf1c06139abdae307abb59b89a8315590de220e215d98b8022","source":{"kind":"arxiv","id":"1605.01333","version":1},"attestation_state":"computed","paper":{"title":"Minimax Estimation of the Volume of a Set with Smooth Boundary","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ME","stat.TH"],"primary_cat":"math.ST","authors_text":"Alberto Rodr\\'iguez-Casal, Beatriz Pateiro-L\\'opez, Ery Arias-Castro","submitted_at":"2016-05-04T16:21:08Z","abstract_excerpt":"We consider the problem of estimating the volume of a compact domain in a Euclidean space based on a uniform sample from the domain. We assume the domain has a boundary with positive reach. We propose a data splitting approach to correct the bias of the plug-in estimator based on the sample alpha-convex hull. We show that this simple estimator achieves a minimax lower bound that we derive. Some numerical experiments corroborate our theoretical findings."},"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":"1605.01333","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2016-05-04T16:21:08Z","cross_cats_sorted":["stat.ME","stat.TH"],"title_canon_sha256":"36249a253939f12efa53b95a2e87701b5f3237da987da89c4fa15d6509dcf8f0","abstract_canon_sha256":"051837fd52bac20a768bca1cb3a7f7003be3c5a959de42f0b3148f5789ecf875"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:15:37.098041Z","signature_b64":"IyNYnszGfUwde7PoVfQVrXWVsptiBF/tyzbZ7QENG82cK0ZKaLTYCA2RL7wDOwn/JlSN1nTq5iD9RZyjX2fRBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"696efe3414ea8edf1c06139abdae307abb59b89a8315590de220e215d98b8022","last_reissued_at":"2026-05-18T01:15:37.097281Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:15:37.097281Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Minimax Estimation of the Volume of a Set with Smooth Boundary","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ME","stat.TH"],"primary_cat":"math.ST","authors_text":"Alberto Rodr\\'iguez-Casal, Beatriz Pateiro-L\\'opez, Ery Arias-Castro","submitted_at":"2016-05-04T16:21:08Z","abstract_excerpt":"We consider the problem of estimating the volume of a compact domain in a Euclidean space based on a uniform sample from the domain. We assume the domain has a boundary with positive reach. We propose a data splitting approach to correct the bias of the plug-in estimator based on the sample alpha-convex hull. We show that this simple estimator achieves a minimax lower bound that we derive. Some numerical experiments corroborate our theoretical findings."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.01333","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1605.01333","created_at":"2026-05-18T01:15:37.097413+00:00"},{"alias_kind":"arxiv_version","alias_value":"1605.01333v1","created_at":"2026-05-18T01:15:37.097413+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.01333","created_at":"2026-05-18T01:15:37.097413+00:00"},{"alias_kind":"pith_short_12","alias_value":"NFXP4NAU5KHN","created_at":"2026-05-18T12:30:32.724797+00:00"},{"alias_kind":"pith_short_16","alias_value":"NFXP4NAU5KHN6HAG","created_at":"2026-05-18T12:30:32.724797+00:00"},{"alias_kind":"pith_short_8","alias_value":"NFXP4NAU","created_at":"2026-05-18T12:30:32.724797+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/NFXP4NAU5KHN6HAGCONL3LRQPK","json":"https://pith.science/pith/NFXP4NAU5KHN6HAGCONL3LRQPK.json","graph_json":"https://pith.science/api/pith-number/NFXP4NAU5KHN6HAGCONL3LRQPK/graph.json","events_json":"https://pith.science/api/pith-number/NFXP4NAU5KHN6HAGCONL3LRQPK/events.json","paper":"https://pith.science/paper/NFXP4NAU"},"agent_actions":{"view_html":"https://pith.science/pith/NFXP4NAU5KHN6HAGCONL3LRQPK","download_json":"https://pith.science/pith/NFXP4NAU5KHN6HAGCONL3LRQPK.json","view_paper":"https://pith.science/paper/NFXP4NAU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1605.01333&json=true","fetch_graph":"https://pith.science/api/pith-number/NFXP4NAU5KHN6HAGCONL3LRQPK/graph.json","fetch_events":"https://pith.science/api/pith-number/NFXP4NAU5KHN6HAGCONL3LRQPK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NFXP4NAU5KHN6HAGCONL3LRQPK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NFXP4NAU5KHN6HAGCONL3LRQPK/action/storage_attestation","attest_author":"https://pith.science/pith/NFXP4NAU5KHN6HAGCONL3LRQPK/action/author_attestation","sign_citation":"https://pith.science/pith/NFXP4NAU5KHN6HAGCONL3LRQPK/action/citation_signature","submit_replication":"https://pith.science/pith/NFXP4NAU5KHN6HAGCONL3LRQPK/action/replication_record"}},"created_at":"2026-05-18T01:15:37.097413+00:00","updated_at":"2026-05-18T01:15:37.097413+00:00"}