{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:MG2FO3I5R7FNKMA5EEHVFI6VGZ","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":"ea4e767e39548597c6108a89c67ef449f7b1e1a08a40d1b74ec9ca086b343b84","cross_cats_sorted":["stat.TH"],"license":"","primary_cat":"math.ST","submitted_at":"2007-08-01T17:01:53Z","title_canon_sha256":"ab844cd4c0dda27556be58dca3494cad69df22ebab6d09b4109b83804db177dd"},"schema_version":"1.0","source":{"id":"0708.0197","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0708.0197","created_at":"2026-05-18T04:09:15Z"},{"alias_kind":"arxiv_version","alias_value":"0708.0197v1","created_at":"2026-05-18T04:09:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0708.0197","created_at":"2026-05-18T04:09:15Z"},{"alias_kind":"pith_short_12","alias_value":"MG2FO3I5R7FN","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"MG2FO3I5R7FNKMA5","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"MG2FO3I5","created_at":"2026-05-18T12:25:55Z"}],"graph_snapshots":[{"event_id":"sha256:2f42ee563635db2bb24afafd428779ab0b8dafdbfbb35b526fcaa6640a6eb6f3","target":"graph","created_at":"2026-05-18T04:09:15Z","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":"This paper introduces a version of empirical likelihood based on the periodogram and spectral estimating equations. This formulation handles dependent data through a data transformation (i.e., a Fourier transform) and is developed in terms of the spectral distribution rather than a time domain probability distribution. The asymptotic properties of frequency domain empirical likelihood are studied for linear time processes exhibiting both short- and long-range dependence. The method results in likelihood ratios which can be used to build nonparametric, asymptotically correct confidence regions ","authors_text":"Daniel J. Nordman, Soumendra N. Lahiri","cross_cats":["stat.TH"],"headline":"","license":"","primary_cat":"math.ST","submitted_at":"2007-08-01T17:01:53Z","title":"A frequency domain empirical likelihood for short- and long-range dependence"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0708.0197","kind":"arxiv","version":1},"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":"sha256:8cd3b24aa7d0641351063095f22cd024387f0c20241280f449db2868a1a47ef3","target":"record","created_at":"2026-05-18T04:09:15Z","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":"ea4e767e39548597c6108a89c67ef449f7b1e1a08a40d1b74ec9ca086b343b84","cross_cats_sorted":["stat.TH"],"license":"","primary_cat":"math.ST","submitted_at":"2007-08-01T17:01:53Z","title_canon_sha256":"ab844cd4c0dda27556be58dca3494cad69df22ebab6d09b4109b83804db177dd"},"schema_version":"1.0","source":{"id":"0708.0197","kind":"arxiv","version":1}},"canonical_sha256":"61b4576d1d8fcad5301d210f52a3d53666829d202b165c94faa9e64620d2f989","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"61b4576d1d8fcad5301d210f52a3d53666829d202b165c94faa9e64620d2f989","first_computed_at":"2026-05-18T04:09:15.196358Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:09:15.196358Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wF6gd9VvZxEdxbExwBFTQc5es1TYad0MpP78L+ZIfopxXh2ytC3Sy7xNf6bsAiR2Yec2lhpDxTDIG2BpL9ClCg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:09:15.196794Z","signed_message":"canonical_sha256_bytes"},"source_id":"0708.0197","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8cd3b24aa7d0641351063095f22cd024387f0c20241280f449db2868a1a47ef3","sha256:2f42ee563635db2bb24afafd428779ab0b8dafdbfbb35b526fcaa6640a6eb6f3"],"state_sha256":"a1bac786b3898436986243acbb68789e7bfbe0d16f0bd07f046622cf5887ea51"}