{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:4AVPMBN3KGGYO2WRJN37SW77JS","short_pith_number":"pith:4AVPMBN3","schema_version":"1.0","canonical_sha256":"e02af605bb518d876ad14b77f95bff4c9ff6af66deef6f023ac0eba21b23caef","source":{"kind":"arxiv","id":"1812.03240","version":1},"attestation_state":"computed","paper":{"title":"Higher-order Accurate Spectral Density Estimation of Functional Time Series","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Dimitris N. Politis, Tingyi Zhu","submitted_at":"2018-12-07T23:37:16Z","abstract_excerpt":"Under the frequency domain framework for weakly dependent functional time series, a key element is the spectral density kernel which encapsulates the second-order dynamics of the process. We propose a class of spectral density kernel estimators based on the notion of a flat-top kernel. The new class of estimators employs the inverse Fourier transform of a flat-top function as the weight function employed to smooth the periodogram. It is shown that using a flat-top kernel yields a bias reduction and results in a higher-order accuracy in terms of optimizing the integrated mean square error (IMSE"},"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":"1812.03240","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2018-12-07T23:37:16Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"91f6baac24ca9676625560d11923a21c56977f39870b17f74ffc51d1fc663aa6","abstract_canon_sha256":"d9f2a923ad6c37a582e1c365cea9516a4c1eabf0d5256b4b031d7142c5b5bcf4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:58:46.802762Z","signature_b64":"XdjKmulBNpWgblzCC9wThuP+p536Q642lw3CSew+sXVb+TDi2sD/aEETkWWip8A3wQ9qE9HaJZdcPSkaNFGSCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e02af605bb518d876ad14b77f95bff4c9ff6af66deef6f023ac0eba21b23caef","last_reissued_at":"2026-05-17T23:58:46.802229Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:58:46.802229Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Higher-order Accurate Spectral Density Estimation of Functional Time Series","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Dimitris N. Politis, Tingyi Zhu","submitted_at":"2018-12-07T23:37:16Z","abstract_excerpt":"Under the frequency domain framework for weakly dependent functional time series, a key element is the spectral density kernel which encapsulates the second-order dynamics of the process. We propose a class of spectral density kernel estimators based on the notion of a flat-top kernel. The new class of estimators employs the inverse Fourier transform of a flat-top function as the weight function employed to smooth the periodogram. It is shown that using a flat-top kernel yields a bias reduction and results in a higher-order accuracy in terms of optimizing the integrated mean square error (IMSE"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.03240","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":"1812.03240","created_at":"2026-05-17T23:58:46.802327+00:00"},{"alias_kind":"arxiv_version","alias_value":"1812.03240v1","created_at":"2026-05-17T23:58:46.802327+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.03240","created_at":"2026-05-17T23:58:46.802327+00:00"},{"alias_kind":"pith_short_12","alias_value":"4AVPMBN3KGGY","created_at":"2026-05-18T12:32:05.422762+00:00"},{"alias_kind":"pith_short_16","alias_value":"4AVPMBN3KGGYO2WR","created_at":"2026-05-18T12:32:05.422762+00:00"},{"alias_kind":"pith_short_8","alias_value":"4AVPMBN3","created_at":"2026-05-18T12:32:05.422762+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/4AVPMBN3KGGYO2WRJN37SW77JS","json":"https://pith.science/pith/4AVPMBN3KGGYO2WRJN37SW77JS.json","graph_json":"https://pith.science/api/pith-number/4AVPMBN3KGGYO2WRJN37SW77JS/graph.json","events_json":"https://pith.science/api/pith-number/4AVPMBN3KGGYO2WRJN37SW77JS/events.json","paper":"https://pith.science/paper/4AVPMBN3"},"agent_actions":{"view_html":"https://pith.science/pith/4AVPMBN3KGGYO2WRJN37SW77JS","download_json":"https://pith.science/pith/4AVPMBN3KGGYO2WRJN37SW77JS.json","view_paper":"https://pith.science/paper/4AVPMBN3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1812.03240&json=true","fetch_graph":"https://pith.science/api/pith-number/4AVPMBN3KGGYO2WRJN37SW77JS/graph.json","fetch_events":"https://pith.science/api/pith-number/4AVPMBN3KGGYO2WRJN37SW77JS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4AVPMBN3KGGYO2WRJN37SW77JS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4AVPMBN3KGGYO2WRJN37SW77JS/action/storage_attestation","attest_author":"https://pith.science/pith/4AVPMBN3KGGYO2WRJN37SW77JS/action/author_attestation","sign_citation":"https://pith.science/pith/4AVPMBN3KGGYO2WRJN37SW77JS/action/citation_signature","submit_replication":"https://pith.science/pith/4AVPMBN3KGGYO2WRJN37SW77JS/action/replication_record"}},"created_at":"2026-05-17T23:58:46.802327+00:00","updated_at":"2026-05-17T23:58:46.802327+00:00"}