{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:Q4HO4IJ3ZL42BBS2F4YTMEDB2H","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":"8698c5448190713ff9d226dcdb885a21bbc97c8822936b47466118dbf955e06d","cross_cats_sorted":["stat.ME","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2016-05-04T21:22:50Z","title_canon_sha256":"34f26e30c0973e92afa7d5693bc22e6064553bee85dd1bc2f48b6855441e4538"},"schema_version":"1.0","source":{"id":"1605.01440","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.01440","created_at":"2026-05-18T00:27:53Z"},{"alias_kind":"arxiv_version","alias_value":"1605.01440v2","created_at":"2026-05-18T00:27:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.01440","created_at":"2026-05-18T00:27:53Z"},{"alias_kind":"pith_short_12","alias_value":"Q4HO4IJ3ZL42","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_16","alias_value":"Q4HO4IJ3ZL42BBS2","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_8","alias_value":"Q4HO4IJ3","created_at":"2026-05-18T12:30:39Z"}],"graph_snapshots":[{"event_id":"sha256:de9977e32837d760fab09987ada3429061a93e97e9b770f58d53f325f5a89b5c","target":"graph","created_at":"2026-05-18T00:27:53Z","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"},"paper":{"abstract_excerpt":"Consider the multiple linear regression model $y_{i} = \\boldsymbol{x}'_{i} \\boldsymbol{\\beta} + \\epsilon_{i}$, where $\\epsilon_i$'s are independent and identically distributed random variables, $\\mathbf{x}_i$'s are known design vectors and $\\boldsymbol{\\beta}$ is the $p \\times 1$ vector of parameters. An effective way of approximating the distribution of the M-estimator $\\boldsymbol{\\bar{\\beta}}_n$, after proper centering and scaling, is the Perturbation Bootstrap Method. In this current work, second order results of this non-naive bootstrap method have been investigated. Second order correctn","authors_text":"Debraj Das, Soumendra Nath Lahiri","cross_cats":["stat.ME","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2016-05-04T21:22:50Z","title":"Second Order Correctness of Perturbation Bootstrap M-Estimator of Multiple Linear Regression Parameter"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.01440","kind":"arxiv","version":2},"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:ea7cdd84ec8ba59e69c840856703c97c67a44f142ffd9835232493a470e0e88d","target":"record","created_at":"2026-05-18T00:27:53Z","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":"8698c5448190713ff9d226dcdb885a21bbc97c8822936b47466118dbf955e06d","cross_cats_sorted":["stat.ME","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2016-05-04T21:22:50Z","title_canon_sha256":"34f26e30c0973e92afa7d5693bc22e6064553bee85dd1bc2f48b6855441e4538"},"schema_version":"1.0","source":{"id":"1605.01440","kind":"arxiv","version":2}},"canonical_sha256":"870eee213bcaf9a0865a2f31361061d1cd2ba69b0f626548de759d1b60c3ae04","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"870eee213bcaf9a0865a2f31361061d1cd2ba69b0f626548de759d1b60c3ae04","first_computed_at":"2026-05-18T00:27:53.295567Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:27:53.295567Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ouUZaVAbHwdwQHAFEkZuPonocLyCDcf6UjkAV0BoV62+136TI8agenAAMCmduH9c4o6pNMIq06NYoULTuaiACg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:27:53.296082Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.01440","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ea7cdd84ec8ba59e69c840856703c97c67a44f142ffd9835232493a470e0e88d","sha256:de9977e32837d760fab09987ada3429061a93e97e9b770f58d53f325f5a89b5c"],"state_sha256":"7fd37c2bdc38428bae35e544bdac78407d62b4557eea97a0c834abadbea54f98"}