{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:2IF5IO5LJJC7Y7LERSTPMLSTYJ","short_pith_number":"pith:2IF5IO5L","canonical_record":{"source":{"id":"1710.05963","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2017-10-16T19:25:18Z","cross_cats_sorted":["math.PR","stat.AP","stat.TH"],"title_canon_sha256":"80b2fb5fe7a3d4b09d36a98d9af69b7020a696556c26cb61eb7b961fd33a4c58","abstract_canon_sha256":"5043f33b25eafce8316252ec17bf9ea32f5a20407a1f44a00f776490e31eff8a"},"schema_version":"1.0"},"canonical_sha256":"d20bd43bab4a45fc7d648ca6f62e53c2451714635beedffa4ef4c8cf17bd12ea","source":{"kind":"arxiv","id":"1710.05963","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.05963","created_at":"2026-05-17T23:43:18Z"},{"alias_kind":"arxiv_version","alias_value":"1710.05963v3","created_at":"2026-05-17T23:43:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.05963","created_at":"2026-05-17T23:43:18Z"},{"alias_kind":"pith_short_12","alias_value":"2IF5IO5LJJC7","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_16","alias_value":"2IF5IO5LJJC7Y7LE","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_8","alias_value":"2IF5IO5L","created_at":"2026-05-18T12:30:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:2IF5IO5LJJC7Y7LERSTPMLSTYJ","target":"record","payload":{"canonical_record":{"source":{"id":"1710.05963","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2017-10-16T19:25:18Z","cross_cats_sorted":["math.PR","stat.AP","stat.TH"],"title_canon_sha256":"80b2fb5fe7a3d4b09d36a98d9af69b7020a696556c26cb61eb7b961fd33a4c58","abstract_canon_sha256":"5043f33b25eafce8316252ec17bf9ea32f5a20407a1f44a00f776490e31eff8a"},"schema_version":"1.0"},"canonical_sha256":"d20bd43bab4a45fc7d648ca6f62e53c2451714635beedffa4ef4c8cf17bd12ea","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:43:18.419150Z","signature_b64":"5wXVvcojq/rvj823A98Z1O5Do+lkCCDpPIrTBrU/KQCBqme58hCqVTRhuCbhHXoV8zaqsw3SguVQgpAqFlwsBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d20bd43bab4a45fc7d648ca6f62e53c2451714635beedffa4ef4c8cf17bd12ea","last_reissued_at":"2026-05-17T23:43:18.418537Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:43:18.418537Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1710.05963","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:43:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"a/nhjHxYTs88B5WEzYNlRsqwEr24j3A5RSBEmR+8bboliH05nkMBVouoTGEgkWJr5Du34XKsDOrN367RESNoBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-24T00:07:55.917583Z"},"content_sha256":"c5eb0a4b06fca4c1c5b29f6e29553fe4c1df5d899e818f8ea34d7eb85d8ba90e","schema_version":"1.0","event_id":"sha256:c5eb0a4b06fca4c1c5b29f6e29553fe4c1df5d899e818f8ea34d7eb85d8ba90e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:2IF5IO5LJJC7Y7LERSTPMLSTYJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Asymptotic distribution of least squares estimators for linear models with dependent errors : regular designs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR","stat.AP","stat.TH"],"primary_cat":"math.ST","authors_text":"Emmanuel Caron, Sophie Dede","submitted_at":"2017-10-16T19:25:18Z","abstract_excerpt":"In this paper, we consider the usual linear regression model in the case where the error process is assumed strictly stationary. We use a result from Hannan, who proved a Central Limit Theorem for the usual least squares estimator under general conditions on the design and on the error process. We show that for a large class of designs, the asymptotic covariance matrix is as simple as the independent and identically distributed case. We then estimate the covariance matrix using an estimator of the spectral density whose consistency is proved under very mild conditions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.05963","kind":"arxiv","version":3},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:43:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gux5LQvzN8xFq+TjYZpVNaGmYTCRZGsDLXjYINok2CIE8nB0KljOWd3J98XpAPAYDxHvPwVh8513XrtbtnaWDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-24T00:07:55.917882Z"},"content_sha256":"9654b603ed577d73e62ca46fc27033232f85d8fd627a849f375db9044082d393","schema_version":"1.0","event_id":"sha256:9654b603ed577d73e62ca46fc27033232f85d8fd627a849f375db9044082d393"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2IF5IO5LJJC7Y7LERSTPMLSTYJ/bundle.json","state_url":"https://pith.science/pith/2IF5IO5LJJC7Y7LERSTPMLSTYJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2IF5IO5LJJC7Y7LERSTPMLSTYJ/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-24T00:07:55Z","links":{"resolver":"https://pith.science/pith/2IF5IO5LJJC7Y7LERSTPMLSTYJ","bundle":"https://pith.science/pith/2IF5IO5LJJC7Y7LERSTPMLSTYJ/bundle.json","state":"https://pith.science/pith/2IF5IO5LJJC7Y7LERSTPMLSTYJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2IF5IO5LJJC7Y7LERSTPMLSTYJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:2IF5IO5LJJC7Y7LERSTPMLSTYJ","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":"5043f33b25eafce8316252ec17bf9ea32f5a20407a1f44a00f776490e31eff8a","cross_cats_sorted":["math.PR","stat.AP","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2017-10-16T19:25:18Z","title_canon_sha256":"80b2fb5fe7a3d4b09d36a98d9af69b7020a696556c26cb61eb7b961fd33a4c58"},"schema_version":"1.0","source":{"id":"1710.05963","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.05963","created_at":"2026-05-17T23:43:18Z"},{"alias_kind":"arxiv_version","alias_value":"1710.05963v3","created_at":"2026-05-17T23:43:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.05963","created_at":"2026-05-17T23:43:18Z"},{"alias_kind":"pith_short_12","alias_value":"2IF5IO5LJJC7","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_16","alias_value":"2IF5IO5LJJC7Y7LE","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_8","alias_value":"2IF5IO5L","created_at":"2026-05-18T12:30:55Z"}],"graph_snapshots":[{"event_id":"sha256:9654b603ed577d73e62ca46fc27033232f85d8fd627a849f375db9044082d393","target":"graph","created_at":"2026-05-17T23:43:18Z","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":"In this paper, we consider the usual linear regression model in the case where the error process is assumed strictly stationary. We use a result from Hannan, who proved a Central Limit Theorem for the usual least squares estimator under general conditions on the design and on the error process. We show that for a large class of designs, the asymptotic covariance matrix is as simple as the independent and identically distributed case. We then estimate the covariance matrix using an estimator of the spectral density whose consistency is proved under very mild conditions.","authors_text":"Emmanuel Caron, Sophie Dede","cross_cats":["math.PR","stat.AP","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2017-10-16T19:25:18Z","title":"Asymptotic distribution of least squares estimators for linear models with dependent errors : regular designs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.05963","kind":"arxiv","version":3},"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:c5eb0a4b06fca4c1c5b29f6e29553fe4c1df5d899e818f8ea34d7eb85d8ba90e","target":"record","created_at":"2026-05-17T23:43:18Z","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":"5043f33b25eafce8316252ec17bf9ea32f5a20407a1f44a00f776490e31eff8a","cross_cats_sorted":["math.PR","stat.AP","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2017-10-16T19:25:18Z","title_canon_sha256":"80b2fb5fe7a3d4b09d36a98d9af69b7020a696556c26cb61eb7b961fd33a4c58"},"schema_version":"1.0","source":{"id":"1710.05963","kind":"arxiv","version":3}},"canonical_sha256":"d20bd43bab4a45fc7d648ca6f62e53c2451714635beedffa4ef4c8cf17bd12ea","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d20bd43bab4a45fc7d648ca6f62e53c2451714635beedffa4ef4c8cf17bd12ea","first_computed_at":"2026-05-17T23:43:18.418537Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:43:18.418537Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5wXVvcojq/rvj823A98Z1O5Do+lkCCDpPIrTBrU/KQCBqme58hCqVTRhuCbhHXoV8zaqsw3SguVQgpAqFlwsBQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:43:18.419150Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.05963","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c5eb0a4b06fca4c1c5b29f6e29553fe4c1df5d899e818f8ea34d7eb85d8ba90e","sha256:9654b603ed577d73e62ca46fc27033232f85d8fd627a849f375db9044082d393"],"state_sha256":"3beb25aa67eeaa51d6b431fce572bbcf924b2d1daaecaf03974e4644054fece0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JWZRPxfVkEFNmwO/bhf09rxQlMj3eaV+AAzr6AQk7Rpui82NYmSgqpdWlrGGRxxbGAPv7qmJizLEjVIHm7GCDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-24T00:07:55.921175Z","bundle_sha256":"72f42465681f61c4bc7f5cd182d9be18582b81e1c87bf87fc01e7210e54ae7fb"}}