{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:422ENRGMLUFTJMQAA5EIAEZID5","short_pith_number":"pith:422ENRGM","canonical_record":{"source":{"id":"1804.09941","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2018-04-26T08:48:14Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"5d02d66dc8a55c38d2177e738adb7013bbcf717427cf7e9f73c3646d7593ea33","abstract_canon_sha256":"b7566af89abfc701365231321a28a3f2b5b81080915e9daf27dd6e0d0034c5aa"},"schema_version":"1.0"},"canonical_sha256":"e6b446c4cc5d0b34b20007488013281f56960768a7cecefd8bc06b4f615fe153","source":{"kind":"arxiv","id":"1804.09941","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.09941","created_at":"2026-05-18T00:17:25Z"},{"alias_kind":"arxiv_version","alias_value":"1804.09941v1","created_at":"2026-05-18T00:17:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.09941","created_at":"2026-05-18T00:17:25Z"},{"alias_kind":"pith_short_12","alias_value":"422ENRGMLUFT","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_16","alias_value":"422ENRGMLUFTJMQA","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_8","alias_value":"422ENRGM","created_at":"2026-05-18T12:32:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:422ENRGMLUFTJMQAA5EIAEZID5","target":"record","payload":{"canonical_record":{"source":{"id":"1804.09941","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2018-04-26T08:48:14Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"5d02d66dc8a55c38d2177e738adb7013bbcf717427cf7e9f73c3646d7593ea33","abstract_canon_sha256":"b7566af89abfc701365231321a28a3f2b5b81080915e9daf27dd6e0d0034c5aa"},"schema_version":"1.0"},"canonical_sha256":"e6b446c4cc5d0b34b20007488013281f56960768a7cecefd8bc06b4f615fe153","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:17:25.685674Z","signature_b64":"6SNn+nK49qWJcTwcMtUEea7VjstpyM1fzYR7+IA7DDLJBEf0Hns638DsaLI5jq/R3z7IVHRsQw4d0Tkm/mpPDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e6b446c4cc5d0b34b20007488013281f56960768a7cecefd8bc06b4f615fe153","last_reissued_at":"2026-05-18T00:17:25.684867Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:17:25.684867Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1804.09941","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":"2026-05-18T00:17:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fUYs35qAeLBMkp69XMFsbpQGbZIOlPFjyJK8MYHhcKWhiQpcksdlDrjQfng4x+L9AEDPnevMNI4+ms3x6/7YBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T04:57:31.913743Z"},"content_sha256":"3349ecbe252b5856f7136d936cb81409a21d263b929b7b9acb49203ad88c51aa","schema_version":"1.0","event_id":"sha256:3349ecbe252b5856f7136d936cb81409a21d263b929b7b9acb49203ad88c51aa"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:422ENRGMLUFTJMQAA5EIAEZID5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Measuring the Variability of Small Area Estimators in a Multivariate Fay-Herriot Model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Tatsuya Kubokawa, Tsubasa Ito","submitted_at":"2018-04-26T08:48:14Z","abstract_excerpt":"This paper is concerned with the small area estimation in the multivariate Fay-Herriot model where covariance matrix of random effects are fully unknown. The covariance matrix is estimated by a Prasad-Rao type consistent estimator, and the empirical best linear un- biased predictor (EBLUP) of a vector of small area characteristics is provided. When the EBLUP is measured in terms of a mean squared error matrix (MSEM), a second-order approximation of MSEM of the EBLUP and a second-order unbiased estimator of the MSEM is derived analytically in closed forms. The performance is investigated throug"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.09941","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":"2026-05-18T00:17:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/t7cMRrVxyUZRyVDLt6y6qHN5Wa4GLTQDtzGZOeskkfyfvW0n9RZsF4XkpZWMbdf9K7D1wTSmrf/5k4FcO96Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T04:57:31.914090Z"},"content_sha256":"ca62aff16781b59b04ccbe5b56807cbc731dff83e18c5e9269db8fb9b2e4cfd4","schema_version":"1.0","event_id":"sha256:ca62aff16781b59b04ccbe5b56807cbc731dff83e18c5e9269db8fb9b2e4cfd4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/422ENRGMLUFTJMQAA5EIAEZID5/bundle.json","state_url":"https://pith.science/pith/422ENRGMLUFTJMQAA5EIAEZID5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/422ENRGMLUFTJMQAA5EIAEZID5/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":"2026-06-12T04:57:31Z","links":{"resolver":"https://pith.science/pith/422ENRGMLUFTJMQAA5EIAEZID5","bundle":"https://pith.science/pith/422ENRGMLUFTJMQAA5EIAEZID5/bundle.json","state":"https://pith.science/pith/422ENRGMLUFTJMQAA5EIAEZID5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/422ENRGMLUFTJMQAA5EIAEZID5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:422ENRGMLUFTJMQAA5EIAEZID5","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":"b7566af89abfc701365231321a28a3f2b5b81080915e9daf27dd6e0d0034c5aa","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2018-04-26T08:48:14Z","title_canon_sha256":"5d02d66dc8a55c38d2177e738adb7013bbcf717427cf7e9f73c3646d7593ea33"},"schema_version":"1.0","source":{"id":"1804.09941","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.09941","created_at":"2026-05-18T00:17:25Z"},{"alias_kind":"arxiv_version","alias_value":"1804.09941v1","created_at":"2026-05-18T00:17:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.09941","created_at":"2026-05-18T00:17:25Z"},{"alias_kind":"pith_short_12","alias_value":"422ENRGMLUFT","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_16","alias_value":"422ENRGMLUFTJMQA","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_8","alias_value":"422ENRGM","created_at":"2026-05-18T12:32:05Z"}],"graph_snapshots":[{"event_id":"sha256:ca62aff16781b59b04ccbe5b56807cbc731dff83e18c5e9269db8fb9b2e4cfd4","target":"graph","created_at":"2026-05-18T00:17:25Z","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 is concerned with the small area estimation in the multivariate Fay-Herriot model where covariance matrix of random effects are fully unknown. The covariance matrix is estimated by a Prasad-Rao type consistent estimator, and the empirical best linear un- biased predictor (EBLUP) of a vector of small area characteristics is provided. When the EBLUP is measured in terms of a mean squared error matrix (MSEM), a second-order approximation of MSEM of the EBLUP and a second-order unbiased estimator of the MSEM is derived analytically in closed forms. The performance is investigated throug","authors_text":"Tatsuya Kubokawa, Tsubasa Ito","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2018-04-26T08:48:14Z","title":"On Measuring the Variability of Small Area Estimators in a Multivariate Fay-Herriot Model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.09941","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":"sha256:3349ecbe252b5856f7136d936cb81409a21d263b929b7b9acb49203ad88c51aa","target":"record","created_at":"2026-05-18T00:17:25Z","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":"b7566af89abfc701365231321a28a3f2b5b81080915e9daf27dd6e0d0034c5aa","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2018-04-26T08:48:14Z","title_canon_sha256":"5d02d66dc8a55c38d2177e738adb7013bbcf717427cf7e9f73c3646d7593ea33"},"schema_version":"1.0","source":{"id":"1804.09941","kind":"arxiv","version":1}},"canonical_sha256":"e6b446c4cc5d0b34b20007488013281f56960768a7cecefd8bc06b4f615fe153","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e6b446c4cc5d0b34b20007488013281f56960768a7cecefd8bc06b4f615fe153","first_computed_at":"2026-05-18T00:17:25.684867Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:17:25.684867Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6SNn+nK49qWJcTwcMtUEea7VjstpyM1fzYR7+IA7DDLJBEf0Hns638DsaLI5jq/R3z7IVHRsQw4d0Tkm/mpPDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:17:25.685674Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.09941","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3349ecbe252b5856f7136d936cb81409a21d263b929b7b9acb49203ad88c51aa","sha256:ca62aff16781b59b04ccbe5b56807cbc731dff83e18c5e9269db8fb9b2e4cfd4"],"state_sha256":"2adee6dbc49b871998be867c7f8b92490c9ee068c29a2f24df7dd453bd11f021"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XBXrZ9sz2/d1or8rniKR0zziA0u+qVVzKQzF8BZREy9DzvhPw3pX4ZOit0ZOGGwjHv2RzTG4lWa9GhJpPip0DA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-12T04:57:31.916240Z","bundle_sha256":"b91216682e00a03f70e0160e90829a77ae8aeccf8ae5762875f90fea90141965"}}