{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:QHUX6VJDUUGZXMI3PINRAWX7PW","short_pith_number":"pith:QHUX6VJD","schema_version":"1.0","canonical_sha256":"81e97f5523a50d9bb11b7a1b105aff7db15d0c0d4b0d9a164b7460da4ca5c7cc","source":{"kind":"arxiv","id":"1102.5212","version":1},"attestation_state":"computed","paper":{"title":"Functional linear regression via canonical analysis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Guozhong He, Hans-Georg M\\\"uller, Jane-Ling Wang, Wenjing Yang","submitted_at":"2011-02-25T11:13:43Z","abstract_excerpt":"We study regression models for the situation where both dependent and independent variables are square-integrable stochastic processes. Questions concerning the definition and existence of the corresponding functional linear regression models and some basic properties are explored for this situation. We derive a representation of the regression parameter function in terms of the canonical components of the processes involved. This representation establishes a connection between functional regression and functional canonical analysis and suggests alternative approaches for the implementation of"},"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":"1102.5212","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2011-02-25T11:13:43Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"237fbbf398576edef7fed07fb2a6c02f10e9e8a827d5965356bf148eb6251c6f","abstract_canon_sha256":"7209447abd06da64731a6761ce853e86bff68aee63a05e52aa96e5fef558a5e2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:27:55.964157Z","signature_b64":"bghfdB9pcQI6/EgC2hAwyy1FzNBt2O3AG0v3el8iF/kCy3mf4lveiAH25/5uV3h6hIU+YrFJQqkCX6w3OlBPDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"81e97f5523a50d9bb11b7a1b105aff7db15d0c0d4b0d9a164b7460da4ca5c7cc","last_reissued_at":"2026-05-18T04:27:55.963450Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:27:55.963450Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Functional linear regression via canonical analysis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Guozhong He, Hans-Georg M\\\"uller, Jane-Ling Wang, Wenjing Yang","submitted_at":"2011-02-25T11:13:43Z","abstract_excerpt":"We study regression models for the situation where both dependent and independent variables are square-integrable stochastic processes. Questions concerning the definition and existence of the corresponding functional linear regression models and some basic properties are explored for this situation. We derive a representation of the regression parameter function in terms of the canonical components of the processes involved. This representation establishes a connection between functional regression and functional canonical analysis and suggests alternative approaches for the implementation of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.5212","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":"1102.5212","created_at":"2026-05-18T04:27:55.963568+00:00"},{"alias_kind":"arxiv_version","alias_value":"1102.5212v1","created_at":"2026-05-18T04:27:55.963568+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.5212","created_at":"2026-05-18T04:27:55.963568+00:00"},{"alias_kind":"pith_short_12","alias_value":"QHUX6VJDUUGZ","created_at":"2026-05-18T12:26:39.201973+00:00"},{"alias_kind":"pith_short_16","alias_value":"QHUX6VJDUUGZXMI3","created_at":"2026-05-18T12:26:39.201973+00:00"},{"alias_kind":"pith_short_8","alias_value":"QHUX6VJD","created_at":"2026-05-18T12:26:39.201973+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/QHUX6VJDUUGZXMI3PINRAWX7PW","json":"https://pith.science/pith/QHUX6VJDUUGZXMI3PINRAWX7PW.json","graph_json":"https://pith.science/api/pith-number/QHUX6VJDUUGZXMI3PINRAWX7PW/graph.json","events_json":"https://pith.science/api/pith-number/QHUX6VJDUUGZXMI3PINRAWX7PW/events.json","paper":"https://pith.science/paper/QHUX6VJD"},"agent_actions":{"view_html":"https://pith.science/pith/QHUX6VJDUUGZXMI3PINRAWX7PW","download_json":"https://pith.science/pith/QHUX6VJDUUGZXMI3PINRAWX7PW.json","view_paper":"https://pith.science/paper/QHUX6VJD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1102.5212&json=true","fetch_graph":"https://pith.science/api/pith-number/QHUX6VJDUUGZXMI3PINRAWX7PW/graph.json","fetch_events":"https://pith.science/api/pith-number/QHUX6VJDUUGZXMI3PINRAWX7PW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QHUX6VJDUUGZXMI3PINRAWX7PW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QHUX6VJDUUGZXMI3PINRAWX7PW/action/storage_attestation","attest_author":"https://pith.science/pith/QHUX6VJDUUGZXMI3PINRAWX7PW/action/author_attestation","sign_citation":"https://pith.science/pith/QHUX6VJDUUGZXMI3PINRAWX7PW/action/citation_signature","submit_replication":"https://pith.science/pith/QHUX6VJDUUGZXMI3PINRAWX7PW/action/replication_record"}},"created_at":"2026-05-18T04:27:55.963568+00:00","updated_at":"2026-05-18T04:27:55.963568+00:00"}