{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:QBIAIQ32LZOUCN5IZT43WZHQ2Q","short_pith_number":"pith:QBIAIQ32","schema_version":"1.0","canonical_sha256":"805004437a5e5d4137a8ccf9bb64f0d42441a164ebab8f45d2bb4156fe8339f2","source":{"kind":"arxiv","id":"1204.3132","version":4},"attestation_state":"computed","paper":{"title":"The Bias and Efficiency of Incomplete-Data Estimators in Small Univariate Normal Samples","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ME","stat.TH"],"primary_cat":"math.ST","authors_text":"Paul T. von Hippel","submitted_at":"2012-04-14T02:25:58Z","abstract_excerpt":"Widely used methods for analyzing missing data can be biased in small samples. To understand these biases, we evaluate in detail the situation where a small univariate normal sample, with values missing at random, is analyzed using either observed-data maximum likelihood (ML) or multiple imputation (MI). We evaluate two types of MI: the usual Bayesian approach, which we call posterior draw (PD) imputation, and a little-used alternative, which we call ML imputation, in which values are imputed conditionally on an ML estimate. We find that observed-data ML is more efficient and has lower mean sq"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1204.3132","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2012-04-14T02:25:58Z","cross_cats_sorted":["stat.ME","stat.TH"],"title_canon_sha256":"146d2b1fe8e1edf8d844a75e44e1c0de74c845df3be1aed657627ea663269e8f","abstract_canon_sha256":"41bc73809f8ff6d892c00e025ba2e911e4bd179b5f7cc90bc8535ade124e6ed2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:48:01.615381Z","signature_b64":"UUMfocDZaKTivX60zsth6a5MVyVmFGnanh6Z7MgFHq820TRN5cdECdbZ6yONOYk0HVyK6siRWSV0H939L1GXBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"805004437a5e5d4137a8ccf9bb64f0d42441a164ebab8f45d2bb4156fe8339f2","last_reissued_at":"2026-05-18T00:48:01.614756Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:48:01.614756Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Bias and Efficiency of Incomplete-Data Estimators in Small Univariate Normal Samples","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ME","stat.TH"],"primary_cat":"math.ST","authors_text":"Paul T. von Hippel","submitted_at":"2012-04-14T02:25:58Z","abstract_excerpt":"Widely used methods for analyzing missing data can be biased in small samples. To understand these biases, we evaluate in detail the situation where a small univariate normal sample, with values missing at random, is analyzed using either observed-data maximum likelihood (ML) or multiple imputation (MI). We evaluate two types of MI: the usual Bayesian approach, which we call posterior draw (PD) imputation, and a little-used alternative, which we call ML imputation, in which values are imputed conditionally on an ML estimate. We find that observed-data ML is more efficient and has lower mean sq"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.3132","kind":"arxiv","version":4},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1204.3132","created_at":"2026-05-18T00:48:01.614856+00:00"},{"alias_kind":"arxiv_version","alias_value":"1204.3132v4","created_at":"2026-05-18T00:48:01.614856+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.3132","created_at":"2026-05-18T00:48:01.614856+00:00"},{"alias_kind":"pith_short_12","alias_value":"QBIAIQ32LZOU","created_at":"2026-05-18T12:27:18.751474+00:00"},{"alias_kind":"pith_short_16","alias_value":"QBIAIQ32LZOUCN5I","created_at":"2026-05-18T12:27:18.751474+00:00"},{"alias_kind":"pith_short_8","alias_value":"QBIAIQ32","created_at":"2026-05-18T12:27:18.751474+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/QBIAIQ32LZOUCN5IZT43WZHQ2Q","json":"https://pith.science/pith/QBIAIQ32LZOUCN5IZT43WZHQ2Q.json","graph_json":"https://pith.science/api/pith-number/QBIAIQ32LZOUCN5IZT43WZHQ2Q/graph.json","events_json":"https://pith.science/api/pith-number/QBIAIQ32LZOUCN5IZT43WZHQ2Q/events.json","paper":"https://pith.science/paper/QBIAIQ32"},"agent_actions":{"view_html":"https://pith.science/pith/QBIAIQ32LZOUCN5IZT43WZHQ2Q","download_json":"https://pith.science/pith/QBIAIQ32LZOUCN5IZT43WZHQ2Q.json","view_paper":"https://pith.science/paper/QBIAIQ32","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1204.3132&json=true","fetch_graph":"https://pith.science/api/pith-number/QBIAIQ32LZOUCN5IZT43WZHQ2Q/graph.json","fetch_events":"https://pith.science/api/pith-number/QBIAIQ32LZOUCN5IZT43WZHQ2Q/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QBIAIQ32LZOUCN5IZT43WZHQ2Q/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QBIAIQ32LZOUCN5IZT43WZHQ2Q/action/storage_attestation","attest_author":"https://pith.science/pith/QBIAIQ32LZOUCN5IZT43WZHQ2Q/action/author_attestation","sign_citation":"https://pith.science/pith/QBIAIQ32LZOUCN5IZT43WZHQ2Q/action/citation_signature","submit_replication":"https://pith.science/pith/QBIAIQ32LZOUCN5IZT43WZHQ2Q/action/replication_record"}},"created_at":"2026-05-18T00:48:01.614856+00:00","updated_at":"2026-05-18T00:48:01.614856+00:00"}