{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:RD2QNL3STBVW6SVRNHV4LYYT2M","short_pith_number":"pith:RD2QNL3S","canonical_record":{"source":{"id":"1205.6644","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2012-05-30T12:26:48Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"2c5291b3af3cff4f7657a9c362389ae820beb13b98a690c06e59c5dc0995aadc","abstract_canon_sha256":"1f8a9c0f4e9b93eae414ba49d4b815d10d9bde609db09c25a63ec2f8426a3c91"},"schema_version":"1.0"},"canonical_sha256":"88f506af72986b6f4ab169ebc5e313d3272cca50dab9ddbf6cf95325cf246ebf","source":{"kind":"arxiv","id":"1205.6644","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.6644","created_at":"2026-05-18T03:54:38Z"},{"alias_kind":"arxiv_version","alias_value":"1205.6644v1","created_at":"2026-05-18T03:54:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.6644","created_at":"2026-05-18T03:54:38Z"},{"alias_kind":"pith_short_12","alias_value":"RD2QNL3STBVW","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_16","alias_value":"RD2QNL3STBVW6SVR","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_8","alias_value":"RD2QNL3S","created_at":"2026-05-18T12:27:20Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:RD2QNL3STBVW6SVRNHV4LYYT2M","target":"record","payload":{"canonical_record":{"source":{"id":"1205.6644","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2012-05-30T12:26:48Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"2c5291b3af3cff4f7657a9c362389ae820beb13b98a690c06e59c5dc0995aadc","abstract_canon_sha256":"1f8a9c0f4e9b93eae414ba49d4b815d10d9bde609db09c25a63ec2f8426a3c91"},"schema_version":"1.0"},"canonical_sha256":"88f506af72986b6f4ab169ebc5e313d3272cca50dab9ddbf6cf95325cf246ebf","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:54:38.330227Z","signature_b64":"D8Je7KtG5r4+L6RYp32X6bGjQkwxCMEI8MtZUT7v/WLQlPmANjm2abTeVhaGUaJ/TP/TkL3Bsfv8y8Yl1le6Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"88f506af72986b6f4ab169ebc5e313d3272cca50dab9ddbf6cf95325cf246ebf","last_reissued_at":"2026-05-18T03:54:38.329653Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:54:38.329653Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1205.6644","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:54:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1ZVS5+AMpPamyLe5YuuMwQts8Oy/eM6vvZRItQNRQuS2edRwBnj2DoS2L67jibs0livOnxT1E1INIVU8yr8WBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T17:47:08.104835Z"},"content_sha256":"7aa768f15df3be4c5ce9dfda3eee43b43025c03a3bdda8b1df453c17abc7bfea","schema_version":"1.0","event_id":"sha256:7aa768f15df3be4c5ce9dfda3eee43b43025c03a3bdda8b1df453c17abc7bfea"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:RD2QNL3STBVW6SVRNHV4LYYT2M","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Simultaneous confidence bands for Yule-Walker estimators and order selection","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Moritz Jirak","submitted_at":"2012-05-30T12:26:48Z","abstract_excerpt":"Let $\\{X_k,k\\in{\\mathbb{Z}}\\}$ be an autoregressive process of order $q$. Various estimators for the order $q$ and the parameters ${\\bolds \\Theta}_q=(\\theta_1,...,\\theta_q)^T$ are known; the order is usually determined with Akaike's criterion or related modifications, whereas Yule-Walker, Burger or maximum likelihood estimators are used for the parameters ${\\bolds\\Theta}_q$. In this paper, we establish simultaneous confidence bands for the Yule--Walker estimators $\\hat{\\theta}_i$; more precisely, it is shown that the limiting distribution of ${\\max_{1\\leq i\\leq d_n}}|\\hat{\\theta}_i-\\theta_i|$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.6644","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:54:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5sYpR+fZ4mYoP2w8uCcRaWed+exUTRCoHD6TuIjBGVp5v+DrWGbbstDto7aNWyUbuKgtDU4g8yXLi3PTNv+BBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T17:47:08.105182Z"},"content_sha256":"9af1778e8580b9b51b400c8d6ea7aafa509cbd08538efb1ab10791b5d707e068","schema_version":"1.0","event_id":"sha256:9af1778e8580b9b51b400c8d6ea7aafa509cbd08538efb1ab10791b5d707e068"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RD2QNL3STBVW6SVRNHV4LYYT2M/bundle.json","state_url":"https://pith.science/pith/RD2QNL3STBVW6SVRNHV4LYYT2M/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RD2QNL3STBVW6SVRNHV4LYYT2M/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":"2026-06-25T17:47:08Z","links":{"resolver":"https://pith.science/pith/RD2QNL3STBVW6SVRNHV4LYYT2M","bundle":"https://pith.science/pith/RD2QNL3STBVW6SVRNHV4LYYT2M/bundle.json","state":"https://pith.science/pith/RD2QNL3STBVW6SVRNHV4LYYT2M/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RD2QNL3STBVW6SVRNHV4LYYT2M/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:RD2QNL3STBVW6SVRNHV4LYYT2M","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":"1f8a9c0f4e9b93eae414ba49d4b815d10d9bde609db09c25a63ec2f8426a3c91","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2012-05-30T12:26:48Z","title_canon_sha256":"2c5291b3af3cff4f7657a9c362389ae820beb13b98a690c06e59c5dc0995aadc"},"schema_version":"1.0","source":{"id":"1205.6644","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.6644","created_at":"2026-05-18T03:54:38Z"},{"alias_kind":"arxiv_version","alias_value":"1205.6644v1","created_at":"2026-05-18T03:54:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.6644","created_at":"2026-05-18T03:54:38Z"},{"alias_kind":"pith_short_12","alias_value":"RD2QNL3STBVW","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_16","alias_value":"RD2QNL3STBVW6SVR","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_8","alias_value":"RD2QNL3S","created_at":"2026-05-18T12:27:20Z"}],"graph_snapshots":[{"event_id":"sha256:9af1778e8580b9b51b400c8d6ea7aafa509cbd08538efb1ab10791b5d707e068","target":"graph","created_at":"2026-05-18T03:54:38Z","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":"Let $\\{X_k,k\\in{\\mathbb{Z}}\\}$ be an autoregressive process of order $q$. Various estimators for the order $q$ and the parameters ${\\bolds \\Theta}_q=(\\theta_1,...,\\theta_q)^T$ are known; the order is usually determined with Akaike's criterion or related modifications, whereas Yule-Walker, Burger or maximum likelihood estimators are used for the parameters ${\\bolds\\Theta}_q$. In this paper, we establish simultaneous confidence bands for the Yule--Walker estimators $\\hat{\\theta}_i$; more precisely, it is shown that the limiting distribution of ${\\max_{1\\leq i\\leq d_n}}|\\hat{\\theta}_i-\\theta_i|$ ","authors_text":"Moritz Jirak","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2012-05-30T12:26:48Z","title":"Simultaneous confidence bands for Yule-Walker estimators and order selection"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.6644","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":"sha256:7aa768f15df3be4c5ce9dfda3eee43b43025c03a3bdda8b1df453c17abc7bfea","target":"record","created_at":"2026-05-18T03:54:38Z","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":"1f8a9c0f4e9b93eae414ba49d4b815d10d9bde609db09c25a63ec2f8426a3c91","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2012-05-30T12:26:48Z","title_canon_sha256":"2c5291b3af3cff4f7657a9c362389ae820beb13b98a690c06e59c5dc0995aadc"},"schema_version":"1.0","source":{"id":"1205.6644","kind":"arxiv","version":1}},"canonical_sha256":"88f506af72986b6f4ab169ebc5e313d3272cca50dab9ddbf6cf95325cf246ebf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"88f506af72986b6f4ab169ebc5e313d3272cca50dab9ddbf6cf95325cf246ebf","first_computed_at":"2026-05-18T03:54:38.329653Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:54:38.329653Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"D8Je7KtG5r4+L6RYp32X6bGjQkwxCMEI8MtZUT7v/WLQlPmANjm2abTeVhaGUaJ/TP/TkL3Bsfv8y8Yl1le6Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:54:38.330227Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.6644","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7aa768f15df3be4c5ce9dfda3eee43b43025c03a3bdda8b1df453c17abc7bfea","sha256:9af1778e8580b9b51b400c8d6ea7aafa509cbd08538efb1ab10791b5d707e068"],"state_sha256":"47e0c9ca4ae1f1d0741e1dfaec31ee83618132927f6f77b86b55ec92586430a1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"25XPck2NNtIJqFQ/ZmboNmpRYU3Kyf8zqdZMTX3A6J1bPdZOsU7Hh/K7k8diszG/8kJRWWEtf+4K0Y7Dmx5aDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T17:47:08.107260Z","bundle_sha256":"82bda4b5490c8d034ccbaa81b9ebe7b69683ee604de5bf9bf6ed806f948a82ef"}}