{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:OCLFAVP22HS4FJQNAO43YTTFF2","short_pith_number":"pith:OCLFAVP2","schema_version":"1.0","canonical_sha256":"70965055fad1e5c2a60d03b9bc4e652ea023e3d37be6ed06ac10268acba3e9f7","source":{"kind":"arxiv","id":"1211.2780","version":2},"attestation_state":"computed","paper":{"title":"Recursive estimation of nonparametric regression with functional covariate","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Aboubacar Amiri (EQUIPPE), Baba Thiam (EQUIPPE), Christophe Crambes (I3M)","submitted_at":"2012-11-12T20:42:39Z","abstract_excerpt":"The main purpose is to estimate the regression function of a real random variable with functional explanatory variable by using a recursive nonparametric kernel approach. The mean square error and the almost sure convergence of a family of recursive kernel estimates of the regression function are derived. These results are established with rates and precise evaluation of the constant terms. Also, a central limit theorem for this class of estimators is established. The method is evaluated on simulations and real data set studies."},"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":"1211.2780","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2012-11-12T20:42:39Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"611a0c2a0c6f17e6ff2c605bf48b4075d268e8b7613d9120cfb819d8aa8d78c0","abstract_canon_sha256":"785cff207ec93bcb37b062888ba0bdbd9ac77d6f24963a110e8736ccd07a3a52"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:16:40.401229Z","signature_b64":"ecBIlke2WK8lg40Lpp1Lpndff04gGRA/wAV7xEH1SD723Ysgt9TW7i3UOSL+xyfhawRAXHpwGbKjuETzOZV2CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"70965055fad1e5c2a60d03b9bc4e652ea023e3d37be6ed06ac10268acba3e9f7","last_reissued_at":"2026-05-18T03:16:40.400510Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:16:40.400510Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Recursive estimation of nonparametric regression with functional covariate","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Aboubacar Amiri (EQUIPPE), Baba Thiam (EQUIPPE), Christophe Crambes (I3M)","submitted_at":"2012-11-12T20:42:39Z","abstract_excerpt":"The main purpose is to estimate the regression function of a real random variable with functional explanatory variable by using a recursive nonparametric kernel approach. The mean square error and the almost sure convergence of a family of recursive kernel estimates of the regression function are derived. These results are established with rates and precise evaluation of the constant terms. Also, a central limit theorem for this class of estimators is established. The method is evaluated on simulations and real data set studies."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.2780","kind":"arxiv","version":2},"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":"1211.2780","created_at":"2026-05-18T03:16:40.400630+00:00"},{"alias_kind":"arxiv_version","alias_value":"1211.2780v2","created_at":"2026-05-18T03:16:40.400630+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.2780","created_at":"2026-05-18T03:16:40.400630+00:00"},{"alias_kind":"pith_short_12","alias_value":"OCLFAVP22HS4","created_at":"2026-05-18T12:27:16.716162+00:00"},{"alias_kind":"pith_short_16","alias_value":"OCLFAVP22HS4FJQN","created_at":"2026-05-18T12:27:16.716162+00:00"},{"alias_kind":"pith_short_8","alias_value":"OCLFAVP2","created_at":"2026-05-18T12:27:16.716162+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/OCLFAVP22HS4FJQNAO43YTTFF2","json":"https://pith.science/pith/OCLFAVP22HS4FJQNAO43YTTFF2.json","graph_json":"https://pith.science/api/pith-number/OCLFAVP22HS4FJQNAO43YTTFF2/graph.json","events_json":"https://pith.science/api/pith-number/OCLFAVP22HS4FJQNAO43YTTFF2/events.json","paper":"https://pith.science/paper/OCLFAVP2"},"agent_actions":{"view_html":"https://pith.science/pith/OCLFAVP22HS4FJQNAO43YTTFF2","download_json":"https://pith.science/pith/OCLFAVP22HS4FJQNAO43YTTFF2.json","view_paper":"https://pith.science/paper/OCLFAVP2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1211.2780&json=true","fetch_graph":"https://pith.science/api/pith-number/OCLFAVP22HS4FJQNAO43YTTFF2/graph.json","fetch_events":"https://pith.science/api/pith-number/OCLFAVP22HS4FJQNAO43YTTFF2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OCLFAVP22HS4FJQNAO43YTTFF2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OCLFAVP22HS4FJQNAO43YTTFF2/action/storage_attestation","attest_author":"https://pith.science/pith/OCLFAVP22HS4FJQNAO43YTTFF2/action/author_attestation","sign_citation":"https://pith.science/pith/OCLFAVP22HS4FJQNAO43YTTFF2/action/citation_signature","submit_replication":"https://pith.science/pith/OCLFAVP22HS4FJQNAO43YTTFF2/action/replication_record"}},"created_at":"2026-05-18T03:16:40.400630+00:00","updated_at":"2026-05-18T03:16:40.400630+00:00"}