{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2004:YYY4VGTLYDWKXYBSWR2JOC4KW7","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":"f3c18373ab926f9a709502b1c39e5bb23d9d00012f5803e2942977156d06c6d8","cross_cats_sorted":["stat.TH"],"license":"","primary_cat":"math.ST","submitted_at":"2004-06-23T08:03:59Z","title_canon_sha256":"dae766d819debd39a74abb08aa5f3566cee1bfce813cb9caeb012068b48a4662"},"schema_version":"1.0","source":{"id":"math/0406455","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0406455","created_at":"2026-07-04T15:01:53Z"},{"alias_kind":"arxiv_version","alias_value":"math/0406455v1","created_at":"2026-07-04T15:01:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0406455","created_at":"2026-07-04T15:01:53Z"},{"alias_kind":"pith_short_12","alias_value":"YYY4VGTLYDWK","created_at":"2026-07-04T15:01:53Z"},{"alias_kind":"pith_short_16","alias_value":"YYY4VGTLYDWKXYBS","created_at":"2026-07-04T15:01:53Z"},{"alias_kind":"pith_short_8","alias_value":"YYY4VGTL","created_at":"2026-07-04T15:01:53Z"}],"graph_snapshots":[{"event_id":"sha256:957b1d27edc4aca780e614057a383af040a6e8cbc2279ba406e0564a61b797fd","target":"graph","created_at":"2026-07-04T15:01:53Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/math/0406455/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The term ``empirical predictor'' refers to a two-stage predictor of a linear combination of fixed and random effects. In the first stage, a predictor is obtained but it involves unknown parameters; thus, in the second stage, the unknown parameters are replaced by their estimators. In this paper, we consider mean squared errors (MSE) of empirical predictors under a general setup, where ML or REML estimators are used for the second stage. We obtain second-order approximation to the MSE as well as an estimator of the MSE correct to the same order. The general results are applied to mixed linear m","authors_text":"Jiming Jiang, J. N. K. Rao, Kalyan Das","cross_cats":["stat.TH"],"headline":"","license":"","primary_cat":"math.ST","submitted_at":"2004-06-23T08:03:59Z","title":"Mean squared error of empirical predictor"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0406455","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":"sha256:49d27327e103048f2e47ae96c6741dc4d9638df26b345dbd356220504a832208","target":"record","created_at":"2026-07-04T15:01:53Z","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":"f3c18373ab926f9a709502b1c39e5bb23d9d00012f5803e2942977156d06c6d8","cross_cats_sorted":["stat.TH"],"license":"","primary_cat":"math.ST","submitted_at":"2004-06-23T08:03:59Z","title_canon_sha256":"dae766d819debd39a74abb08aa5f3566cee1bfce813cb9caeb012068b48a4662"},"schema_version":"1.0","source":{"id":"math/0406455","kind":"arxiv","version":1}},"canonical_sha256":"c631ca9a6bc0ecabe032b474970b8ab7c64a92ec39825946b6a4f93744b9ecf2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c631ca9a6bc0ecabe032b474970b8ab7c64a92ec39825946b6a4f93744b9ecf2","first_computed_at":"2026-07-04T15:01:53.968217Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:01:53.968217Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"G4DHx5O5p0Htd41GYatsKQAu+fdepEUdiiiqUghEpvXmrmQGUMPlEA1nAQOpVF1iPOPmfJ0nN+WFZ69lgpvMDA==","signature_status":"signed_v1","signed_at":"2026-07-04T15:01:53.968574Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0406455","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:49d27327e103048f2e47ae96c6741dc4d9638df26b345dbd356220504a832208","sha256:957b1d27edc4aca780e614057a383af040a6e8cbc2279ba406e0564a61b797fd"],"state_sha256":"eaad4490ee883f50b5e97477b49ca9ac92076aac054c8cc4e837586e0224b74e"}