{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:JUZTJ4C3D4OSJGOEU3PCFY6RT2","short_pith_number":"pith:JUZTJ4C3","canonical_record":{"source":{"id":"1306.5505","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2013-06-24T03:48:03Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"22e0c193b9a92007b32e413f10c1994f0e059b782f5920942ff439e6eb4213d0","abstract_canon_sha256":"b42003570eaddf3a2be9c3315d32460ce1b68baa0ffeb19cab3fb783db969e84"},"schema_version":"1.0"},"canonical_sha256":"4d3334f05b1f1d2499c4a6de22e3d19ea20fd4144b0abd449d840c4d181ca69f","source":{"kind":"arxiv","id":"1306.5505","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.5505","created_at":"2026-05-18T03:02:34Z"},{"alias_kind":"arxiv_version","alias_value":"1306.5505v3","created_at":"2026-05-18T03:02:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.5505","created_at":"2026-05-18T03:02:34Z"},{"alias_kind":"pith_short_12","alias_value":"JUZTJ4C3D4OS","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"JUZTJ4C3D4OSJGOE","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"JUZTJ4C3","created_at":"2026-05-18T12:27:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:JUZTJ4C3D4OSJGOEU3PCFY6RT2","target":"record","payload":{"canonical_record":{"source":{"id":"1306.5505","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2013-06-24T03:48:03Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"22e0c193b9a92007b32e413f10c1994f0e059b782f5920942ff439e6eb4213d0","abstract_canon_sha256":"b42003570eaddf3a2be9c3315d32460ce1b68baa0ffeb19cab3fb783db969e84"},"schema_version":"1.0"},"canonical_sha256":"4d3334f05b1f1d2499c4a6de22e3d19ea20fd4144b0abd449d840c4d181ca69f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:02:34.856627Z","signature_b64":"60kC1va7cahU5veALiGuh2ZaeaordkFawIRriolvSc0BQWdZVRa33KgA0mO/PP8XaM5KiK2OBg+vVY1bW4fcCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4d3334f05b1f1d2499c4a6de22e3d19ea20fd4144b0abd449d840c4d181ca69f","last_reissued_at":"2026-05-18T03:02:34.856050Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:02:34.856050Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1306.5505","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:02:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oSNlYBmBJJHv4OjDq5IRTHe4a3P+N4w0NG5tSkFO1cw/HJHecB817fbbIwF7zg5PX36yTyH993ovEuk3sSZhDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T02:39:21.570429Z"},"content_sha256":"f29f20fd310be4c3ce50163960116c0e73578296c867e6c6e040bb6d0d7622bb","schema_version":"1.0","event_id":"sha256:f29f20fd310be4c3ce50163960116c0e73578296c867e6c6e040bb6d0d7622bb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:JUZTJ4C3D4OSJGOEU3PCFY6RT2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Asymptotic Properties of Lasso+mLS and Lasso+Ridge in Sparse High-dimensional Linear Regression","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Bin Yu, Hanzhong Liu","submitted_at":"2013-06-24T03:48:03Z","abstract_excerpt":"We study the asymptotic properties of Lasso+mLS and Lasso+Ridge under the sparse high-dimensional linear regression model: Lasso selecting predictors and then modified Least Squares (mLS) or Ridge estimating their coefficients. First, we propose a valid inference procedure for parameter estimation based on parametric residual bootstrap after Lasso+mLS and Lasso+Ridge. Second, we derive the asymptotic unbiasedness of Lasso+mLS and Lasso+Ridge. More specifically, we show that their biases decay at an exponential rate and they can achieve the oracle convergence rate of $s/n$ (where $s$ is the num"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.5505","kind":"arxiv","version":3},"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":"2026-05-18T03:02:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ijf5AV/LfMMlZ6uypTbhcqCJ5K+RGEBJAt7Gs5timoD9ubTNRfGwgwWA4mvSccxOOiMZKa+XRedjjptuQUrLCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T02:39:21.570902Z"},"content_sha256":"798860fa566dffa6abf0087ddca300087ae64b79eb7e90d7ef1cae75961b45cf","schema_version":"1.0","event_id":"sha256:798860fa566dffa6abf0087ddca300087ae64b79eb7e90d7ef1cae75961b45cf"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JUZTJ4C3D4OSJGOEU3PCFY6RT2/bundle.json","state_url":"https://pith.science/pith/JUZTJ4C3D4OSJGOEU3PCFY6RT2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JUZTJ4C3D4OSJGOEU3PCFY6RT2/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":"2026-06-26T02:39:21Z","links":{"resolver":"https://pith.science/pith/JUZTJ4C3D4OSJGOEU3PCFY6RT2","bundle":"https://pith.science/pith/JUZTJ4C3D4OSJGOEU3PCFY6RT2/bundle.json","state":"https://pith.science/pith/JUZTJ4C3D4OSJGOEU3PCFY6RT2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JUZTJ4C3D4OSJGOEU3PCFY6RT2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:JUZTJ4C3D4OSJGOEU3PCFY6RT2","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":"b42003570eaddf3a2be9c3315d32460ce1b68baa0ffeb19cab3fb783db969e84","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2013-06-24T03:48:03Z","title_canon_sha256":"22e0c193b9a92007b32e413f10c1994f0e059b782f5920942ff439e6eb4213d0"},"schema_version":"1.0","source":{"id":"1306.5505","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.5505","created_at":"2026-05-18T03:02:34Z"},{"alias_kind":"arxiv_version","alias_value":"1306.5505v3","created_at":"2026-05-18T03:02:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.5505","created_at":"2026-05-18T03:02:34Z"},{"alias_kind":"pith_short_12","alias_value":"JUZTJ4C3D4OS","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"JUZTJ4C3D4OSJGOE","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"JUZTJ4C3","created_at":"2026-05-18T12:27:49Z"}],"graph_snapshots":[{"event_id":"sha256:798860fa566dffa6abf0087ddca300087ae64b79eb7e90d7ef1cae75961b45cf","target":"graph","created_at":"2026-05-18T03:02:34Z","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":"We study the asymptotic properties of Lasso+mLS and Lasso+Ridge under the sparse high-dimensional linear regression model: Lasso selecting predictors and then modified Least Squares (mLS) or Ridge estimating their coefficients. First, we propose a valid inference procedure for parameter estimation based on parametric residual bootstrap after Lasso+mLS and Lasso+Ridge. Second, we derive the asymptotic unbiasedness of Lasso+mLS and Lasso+Ridge. More specifically, we show that their biases decay at an exponential rate and they can achieve the oracle convergence rate of $s/n$ (where $s$ is the num","authors_text":"Bin Yu, Hanzhong Liu","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2013-06-24T03:48:03Z","title":"Asymptotic Properties of Lasso+mLS and Lasso+Ridge in Sparse High-dimensional Linear Regression"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.5505","kind":"arxiv","version":3},"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:f29f20fd310be4c3ce50163960116c0e73578296c867e6c6e040bb6d0d7622bb","target":"record","created_at":"2026-05-18T03:02:34Z","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":"b42003570eaddf3a2be9c3315d32460ce1b68baa0ffeb19cab3fb783db969e84","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2013-06-24T03:48:03Z","title_canon_sha256":"22e0c193b9a92007b32e413f10c1994f0e059b782f5920942ff439e6eb4213d0"},"schema_version":"1.0","source":{"id":"1306.5505","kind":"arxiv","version":3}},"canonical_sha256":"4d3334f05b1f1d2499c4a6de22e3d19ea20fd4144b0abd449d840c4d181ca69f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4d3334f05b1f1d2499c4a6de22e3d19ea20fd4144b0abd449d840c4d181ca69f","first_computed_at":"2026-05-18T03:02:34.856050Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:02:34.856050Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"60kC1va7cahU5veALiGuh2ZaeaordkFawIRriolvSc0BQWdZVRa33KgA0mO/PP8XaM5KiK2OBg+vVY1bW4fcCA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:02:34.856627Z","signed_message":"canonical_sha256_bytes"},"source_id":"1306.5505","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f29f20fd310be4c3ce50163960116c0e73578296c867e6c6e040bb6d0d7622bb","sha256:798860fa566dffa6abf0087ddca300087ae64b79eb7e90d7ef1cae75961b45cf"],"state_sha256":"a693f2c83ead2b1a9621954541adf2a7f2af72f21f193e2753ee8eac3a8593ed"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0rzr5/5rMvVES9IOJPcI/h1bonl+V3/ua8wWjuqRWXxGNnKb3TVSu2059VgGBNCy07ItRFrc5L9Aj27pU1vvDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T02:39:21.573546Z","bundle_sha256":"86c83d635c1ba64260d08b12fa3bfaaf5030a82aef621edb9e006350fb08e35b"}}