{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:A675GNPYEKI7P3CFEAQMZHTSSL","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":"c4d95e0f2df962ab7a8e19bbab81f4a136c2e259dd128af110b1d7205ea7ad81","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2014-09-02T14:47:03Z","title_canon_sha256":"d86d7bb40c128756403d7384ded7a5e7c792d3eb78b508c71cb5ff6fe05bc1bb"},"schema_version":"1.0","source":{"id":"1409.0733","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.0733","created_at":"2026-05-18T01:12:58Z"},{"alias_kind":"arxiv_version","alias_value":"1409.0733v2","created_at":"2026-05-18T01:12:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.0733","created_at":"2026-05-18T01:12:58Z"},{"alias_kind":"pith_short_12","alias_value":"A675GNPYEKI7","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_16","alias_value":"A675GNPYEKI7P3CF","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_8","alias_value":"A675GNPY","created_at":"2026-05-18T12:28:19Z"}],"graph_snapshots":[{"event_id":"sha256:87484cc6450e241679f9a872d2f8ec66c5642cc09653d0051880bc83281584b0","target":"graph","created_at":"2026-05-18T01:12:58Z","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":"Let $(X_1,\\ldots,X_n)$ be an i.i.d. sequence of random variables in $\\mathbb{R}^d$, $d\\geq 1$. We show that, for any function $\\varphi :\\mathbb{R}^d\\rightarrow\\mathbb{R}$, under regularity conditions, \\[n^ {1/2}\\Biggl(n^{-1}\\sum_{i=1}^n\\frac{\\varphi(X_i)}{\\widehat{f}^(X_i)}- \\int \\varphi(x)\\,dx\\Biggr)\\stackrel{\\mathbb{P}}{\\longrightarrow}0,\\] where $\\widehat{f}$ is the classical 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 $\\widehat{f}=f$. Although this paper highlights some ap","authors_text":"Bernard Delyon, Fran\\c{c}ois Portier","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2014-09-02T14:47:03Z","title":"Integral approximation by kernel smoothing"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.0733","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":"sha256:3a46ac0bbb207f747158cf4c283a4e8152a4a40db6d2dbee351664d54306d8b8","target":"record","created_at":"2026-05-18T01:12:58Z","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":"c4d95e0f2df962ab7a8e19bbab81f4a136c2e259dd128af110b1d7205ea7ad81","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2014-09-02T14:47:03Z","title_canon_sha256":"d86d7bb40c128756403d7384ded7a5e7c792d3eb78b508c71cb5ff6fe05bc1bb"},"schema_version":"1.0","source":{"id":"1409.0733","kind":"arxiv","version":2}},"canonical_sha256":"07bfd335f82291f7ec452020cc9e7292c69f2b8a414a229fba1303ffebd83250","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"07bfd335f82291f7ec452020cc9e7292c69f2b8a414a229fba1303ffebd83250","first_computed_at":"2026-05-18T01:12:58.748621Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:12:58.748621Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eM/gJP8/L6fBwD7tfDsrOn3B1Zo9f5Bownld53aDfjpWntywz92ZrKlk+SwVChnnL9PX7yJvzKhm2ObqqQpYAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:12:58.748960Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.0733","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3a46ac0bbb207f747158cf4c283a4e8152a4a40db6d2dbee351664d54306d8b8","sha256:87484cc6450e241679f9a872d2f8ec66c5642cc09653d0051880bc83281584b0"],"state_sha256":"97bcca25dc9b11046611526daf950b1a27183c86a53885e5bd85e8136fb4c992"}