{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:F23EUXK6VKCB7PO54A3CV5BQWA","short_pith_number":"pith:F23EUXK6","schema_version":"1.0","canonical_sha256":"2eb64a5d5eaa841fbddde0362af430b0178283639fd19581e170fbcacd127b67","source":{"kind":"arxiv","id":"1312.4497","version":1},"attestation_state":"computed","paper":{"title":"On the acceleration of some empirical means with application to nonparametric regression","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Bernard Delyon (IRMAR), Fran\\c{c}ois Portier (IRMAR)","submitted_at":"2013-12-16T20:15:21Z","abstract_excerpt":"Let $(X_1,\\ldots ,X_n)$ be an i.i.d. sequence of random variables in $\\R^d$, $d\\geq 1$, for some function $\\varphi:\\R^d\\r \\R$, under regularity conditions, we show that \\begin{align*} n^{1/2} \\left(n^{-1} \\sum_{i=1}^n \\frac{\\varphi(X_i)}{\\w f^{(i)}(X_i)}-\\int_{} \\varphi(x)dx \\right) \\overset{\\P}{\\lr} 0, \\end{align*} where $\\w f^{(i)}$ is the classical leave-one-out kernel estimator of the density of $X_1$. This result is striking because it speeds up traditional rates, in root $n$, derived from the central limit theorem when $\\w f^{(i)}=f$. As a consequence, it improves the classical Monte Car"},"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":"1312.4497","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2013-12-16T20:15:21Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"54b664665ef58628e82c8b4f8fec4e8998aef83aeafb2e5b3124f2e3d9f964e4","abstract_canon_sha256":"50dd3a5d88b60658a0eb0a2e37f1b331d836e3907ab613b4ab099c819ede84b5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:04:24.580556Z","signature_b64":"+pHSTj86aB4vl/8mvvojG+2Uy53HdGy9ST8mv5s6HwYc/1nTBv8MIyB5pd0TJtb39QKkhW3ODbjQzkdPXp8kBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2eb64a5d5eaa841fbddde0362af430b0178283639fd19581e170fbcacd127b67","last_reissued_at":"2026-05-18T03:04:24.579807Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:04:24.579807Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the acceleration of some empirical means with application to nonparametric regression","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Bernard Delyon (IRMAR), Fran\\c{c}ois Portier (IRMAR)","submitted_at":"2013-12-16T20:15:21Z","abstract_excerpt":"Let $(X_1,\\ldots ,X_n)$ be an i.i.d. sequence of random variables in $\\R^d$, $d\\geq 1$, for some function $\\varphi:\\R^d\\r \\R$, under regularity conditions, we show that \\begin{align*} n^{1/2} \\left(n^{-1} \\sum_{i=1}^n \\frac{\\varphi(X_i)}{\\w f^{(i)}(X_i)}-\\int_{} \\varphi(x)dx \\right) \\overset{\\P}{\\lr} 0, \\end{align*} where $\\w f^{(i)}$ is the classical leave-one-out kernel estimator of the density of $X_1$. This result is striking because it speeds up traditional rates, in root $n$, derived from the central limit theorem when $\\w f^{(i)}=f$. As a consequence, it improves the classical Monte Car"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.4497","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":"1312.4497","created_at":"2026-05-18T03:04:24.579933+00:00"},{"alias_kind":"arxiv_version","alias_value":"1312.4497v1","created_at":"2026-05-18T03:04:24.579933+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.4497","created_at":"2026-05-18T03:04:24.579933+00:00"},{"alias_kind":"pith_short_12","alias_value":"F23EUXK6VKCB","created_at":"2026-05-18T12:27:43.054852+00:00"},{"alias_kind":"pith_short_16","alias_value":"F23EUXK6VKCB7PO5","created_at":"2026-05-18T12:27:43.054852+00:00"},{"alias_kind":"pith_short_8","alias_value":"F23EUXK6","created_at":"2026-05-18T12:27:43.054852+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/F23EUXK6VKCB7PO54A3CV5BQWA","json":"https://pith.science/pith/F23EUXK6VKCB7PO54A3CV5BQWA.json","graph_json":"https://pith.science/api/pith-number/F23EUXK6VKCB7PO54A3CV5BQWA/graph.json","events_json":"https://pith.science/api/pith-number/F23EUXK6VKCB7PO54A3CV5BQWA/events.json","paper":"https://pith.science/paper/F23EUXK6"},"agent_actions":{"view_html":"https://pith.science/pith/F23EUXK6VKCB7PO54A3CV5BQWA","download_json":"https://pith.science/pith/F23EUXK6VKCB7PO54A3CV5BQWA.json","view_paper":"https://pith.science/paper/F23EUXK6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1312.4497&json=true","fetch_graph":"https://pith.science/api/pith-number/F23EUXK6VKCB7PO54A3CV5BQWA/graph.json","fetch_events":"https://pith.science/api/pith-number/F23EUXK6VKCB7PO54A3CV5BQWA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/F23EUXK6VKCB7PO54A3CV5BQWA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/F23EUXK6VKCB7PO54A3CV5BQWA/action/storage_attestation","attest_author":"https://pith.science/pith/F23EUXK6VKCB7PO54A3CV5BQWA/action/author_attestation","sign_citation":"https://pith.science/pith/F23EUXK6VKCB7PO54A3CV5BQWA/action/citation_signature","submit_replication":"https://pith.science/pith/F23EUXK6VKCB7PO54A3CV5BQWA/action/replication_record"}},"created_at":"2026-05-18T03:04:24.579933+00:00","updated_at":"2026-05-18T03:04:24.579933+00:00"}