{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:RQIFLN7YLZWWES2WFNF2FXIJL5","short_pith_number":"pith:RQIFLN7Y","schema_version":"1.0","canonical_sha256":"8c1055b7f85e6d624b562b4ba2dd095f539076fde91d4af97396e701e50bf1c3","source":{"kind":"arxiv","id":"1506.00847","version":1},"attestation_state":"computed","paper":{"title":"Two sample inference for the second-order property of temporally dependent functional data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Xianyang Zhang, Xiaofeng Shao","submitted_at":"2015-06-02T11:39:48Z","abstract_excerpt":"Motivated by the need to statistically quantify the difference between two spatio-temporal datasets that arise in climate downscaling studies, we propose new tests to detect the differences of the covariance operators and their associated characteristics of two functional time series. Our two sample tests are constructed on the basis of functional principal component analysis and self-normalization, the latter of which is a new studentization technique recently developed for the inference of a univariate time series. Compared to the existing tests, our SN-based tests allow for weak dependence "},"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":"1506.00847","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2015-06-02T11:39:48Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"de404954409402130070999d116827107fe42248257e7276e1b69dc33cd220bb","abstract_canon_sha256":"5b399eee7bb78c4fb0ecabe6512f6abcb8ed847206dcb9825ce6eb9eed6048c8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:59:34.333872Z","signature_b64":"4jjJnWCr05QA8XpjNSwTsxPRrDwJlmfxwfR8hBFjpvsvfczROdWd36UXZylDtLtNf0XMdRQyAwBfoqX2fgZGCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8c1055b7f85e6d624b562b4ba2dd095f539076fde91d4af97396e701e50bf1c3","last_reissued_at":"2026-05-18T01:59:34.333262Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:59:34.333262Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Two sample inference for the second-order property of temporally dependent functional data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Xianyang Zhang, Xiaofeng Shao","submitted_at":"2015-06-02T11:39:48Z","abstract_excerpt":"Motivated by the need to statistically quantify the difference between two spatio-temporal datasets that arise in climate downscaling studies, we propose new tests to detect the differences of the covariance operators and their associated characteristics of two functional time series. Our two sample tests are constructed on the basis of functional principal component analysis and self-normalization, the latter of which is a new studentization technique recently developed for the inference of a univariate time series. Compared to the existing tests, our SN-based tests allow for weak dependence "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.00847","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":"1506.00847","created_at":"2026-05-18T01:59:34.333355+00:00"},{"alias_kind":"arxiv_version","alias_value":"1506.00847v1","created_at":"2026-05-18T01:59:34.333355+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.00847","created_at":"2026-05-18T01:59:34.333355+00:00"},{"alias_kind":"pith_short_12","alias_value":"RQIFLN7YLZWW","created_at":"2026-05-18T12:29:39.896362+00:00"},{"alias_kind":"pith_short_16","alias_value":"RQIFLN7YLZWWES2W","created_at":"2026-05-18T12:29:39.896362+00:00"},{"alias_kind":"pith_short_8","alias_value":"RQIFLN7Y","created_at":"2026-05-18T12:29:39.896362+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/RQIFLN7YLZWWES2WFNF2FXIJL5","json":"https://pith.science/pith/RQIFLN7YLZWWES2WFNF2FXIJL5.json","graph_json":"https://pith.science/api/pith-number/RQIFLN7YLZWWES2WFNF2FXIJL5/graph.json","events_json":"https://pith.science/api/pith-number/RQIFLN7YLZWWES2WFNF2FXIJL5/events.json","paper":"https://pith.science/paper/RQIFLN7Y"},"agent_actions":{"view_html":"https://pith.science/pith/RQIFLN7YLZWWES2WFNF2FXIJL5","download_json":"https://pith.science/pith/RQIFLN7YLZWWES2WFNF2FXIJL5.json","view_paper":"https://pith.science/paper/RQIFLN7Y","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1506.00847&json=true","fetch_graph":"https://pith.science/api/pith-number/RQIFLN7YLZWWES2WFNF2FXIJL5/graph.json","fetch_events":"https://pith.science/api/pith-number/RQIFLN7YLZWWES2WFNF2FXIJL5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RQIFLN7YLZWWES2WFNF2FXIJL5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RQIFLN7YLZWWES2WFNF2FXIJL5/action/storage_attestation","attest_author":"https://pith.science/pith/RQIFLN7YLZWWES2WFNF2FXIJL5/action/author_attestation","sign_citation":"https://pith.science/pith/RQIFLN7YLZWWES2WFNF2FXIJL5/action/citation_signature","submit_replication":"https://pith.science/pith/RQIFLN7YLZWWES2WFNF2FXIJL5/action/replication_record"}},"created_at":"2026-05-18T01:59:34.333355+00:00","updated_at":"2026-05-18T01:59:34.333355+00:00"}