{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:4FHJBCNSPZMX7JU6IQ3QGCKCJ6","short_pith_number":"pith:4FHJBCNS","canonical_record":{"source":{"id":"1708.07986","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2017-08-26T15:30:57Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"a8a4f4275357559d2c6d8e6c8e98ed2e58bfb5dd991a45751e4e0a06e284032d","abstract_canon_sha256":"00c905ad9318091c70d723f318849f4dbd8e15c130066a71df08fe07317e89c4"},"schema_version":"1.0"},"canonical_sha256":"e14e9089b27e597fa69e44370309424fa4d36b978023f62717480ee39140f02f","source":{"kind":"arxiv","id":"1708.07986","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.07986","created_at":"2026-05-18T00:07:43Z"},{"alias_kind":"arxiv_version","alias_value":"1708.07986v2","created_at":"2026-05-18T00:07:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.07986","created_at":"2026-05-18T00:07:43Z"},{"alias_kind":"pith_short_12","alias_value":"4FHJBCNSPZMX","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_16","alias_value":"4FHJBCNSPZMX7JU6","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_8","alias_value":"4FHJBCNS","created_at":"2026-05-18T12:30:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:4FHJBCNSPZMX7JU6IQ3QGCKCJ6","target":"record","payload":{"canonical_record":{"source":{"id":"1708.07986","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2017-08-26T15:30:57Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"a8a4f4275357559d2c6d8e6c8e98ed2e58bfb5dd991a45751e4e0a06e284032d","abstract_canon_sha256":"00c905ad9318091c70d723f318849f4dbd8e15c130066a71df08fe07317e89c4"},"schema_version":"1.0"},"canonical_sha256":"e14e9089b27e597fa69e44370309424fa4d36b978023f62717480ee39140f02f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:07:43.718558Z","signature_b64":"laG1zXxiqn9KMP5Lnr0jxfm9gcFBJy4jVixGy/ih/m9adJLqIPuybu+6X1oZkl9K6LufwM65SELRowkSUj2aBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e14e9089b27e597fa69e44370309424fa4d36b978023f62717480ee39140f02f","last_reissued_at":"2026-05-18T00:07:43.717886Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:07:43.717886Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1708.07986","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:07:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lMmpDpeCmXG0ouH6+2ovrLtor2tDOoyFpAS6xVI6DA2kMuQx8S3v5UOwOHnBdJnZOJ3iOYMvIuNm6hfaE351CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T03:10:55.605276Z"},"content_sha256":"d93b875e3fcb40815dbaa6b0d3588952404b512479beb3593072e4c28a7d3b84","schema_version":"1.0","event_id":"sha256:d93b875e3fcb40815dbaa6b0d3588952404b512479beb3593072e4c28a7d3b84"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:4FHJBCNSPZMX7JU6IQ3QGCKCJ6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the efficiency of the de-biased Lasso","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Sara van de Geer","submitted_at":"2017-08-26T15:30:57Z","abstract_excerpt":"We consider the high-dimensional linear regression model $Y = X \\beta^0 + \\epsilon$ with Gaussian noise $\\epsilon$ and Gaussian random design $X$. We assume that $\\Sigma:= E X^T X / n$ is non-singular and write its inverse as $\\Theta := \\Sigma^{-1}$. The parameter of interest is the first component $\\beta_1^0$ of $\\beta^0$. We show that in the high-dimensional case the asymptotic variance of a debiased Lasso estimator can be smaller than $\\Theta_{1,1}$. For some special such cases we establish asymptotic efficiency. The conditions include $\\beta^0$ being sparse and the first column $\\Theta_1$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.07986","kind":"arxiv","version":2},"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":"2026-05-18T00:07:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Huej6uptyVseGCl/oQ96Ev9XXMgFsJU1/xodBs1o3EG0mJGjMdWC82wiIbcis7pAUeeANGQCBt3RfmWapSyzDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T03:10:55.605641Z"},"content_sha256":"5b7520f29932bd5e213cefb3eb178fe1c869d821f8d582bd5baedda65e1bb50b","schema_version":"1.0","event_id":"sha256:5b7520f29932bd5e213cefb3eb178fe1c869d821f8d582bd5baedda65e1bb50b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4FHJBCNSPZMX7JU6IQ3QGCKCJ6/bundle.json","state_url":"https://pith.science/pith/4FHJBCNSPZMX7JU6IQ3QGCKCJ6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4FHJBCNSPZMX7JU6IQ3QGCKCJ6/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":"2026-06-02T03:10:55Z","links":{"resolver":"https://pith.science/pith/4FHJBCNSPZMX7JU6IQ3QGCKCJ6","bundle":"https://pith.science/pith/4FHJBCNSPZMX7JU6IQ3QGCKCJ6/bundle.json","state":"https://pith.science/pith/4FHJBCNSPZMX7JU6IQ3QGCKCJ6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4FHJBCNSPZMX7JU6IQ3QGCKCJ6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:4FHJBCNSPZMX7JU6IQ3QGCKCJ6","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":"00c905ad9318091c70d723f318849f4dbd8e15c130066a71df08fe07317e89c4","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2017-08-26T15:30:57Z","title_canon_sha256":"a8a4f4275357559d2c6d8e6c8e98ed2e58bfb5dd991a45751e4e0a06e284032d"},"schema_version":"1.0","source":{"id":"1708.07986","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.07986","created_at":"2026-05-18T00:07:43Z"},{"alias_kind":"arxiv_version","alias_value":"1708.07986v2","created_at":"2026-05-18T00:07:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.07986","created_at":"2026-05-18T00:07:43Z"},{"alias_kind":"pith_short_12","alias_value":"4FHJBCNSPZMX","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_16","alias_value":"4FHJBCNSPZMX7JU6","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_8","alias_value":"4FHJBCNS","created_at":"2026-05-18T12:30:58Z"}],"graph_snapshots":[{"event_id":"sha256:5b7520f29932bd5e213cefb3eb178fe1c869d821f8d582bd5baedda65e1bb50b","target":"graph","created_at":"2026-05-18T00:07:43Z","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 consider the high-dimensional linear regression model $Y = X \\beta^0 + \\epsilon$ with Gaussian noise $\\epsilon$ and Gaussian random design $X$. We assume that $\\Sigma:= E X^T X / n$ is non-singular and write its inverse as $\\Theta := \\Sigma^{-1}$. The parameter of interest is the first component $\\beta_1^0$ of $\\beta^0$. We show that in the high-dimensional case the asymptotic variance of a debiased Lasso estimator can be smaller than $\\Theta_{1,1}$. For some special such cases we establish asymptotic efficiency. The conditions include $\\beta^0$ being sparse and the first column $\\Theta_1$ ","authors_text":"Sara van de Geer","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2017-08-26T15:30:57Z","title":"On the efficiency of the de-biased Lasso"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.07986","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:d93b875e3fcb40815dbaa6b0d3588952404b512479beb3593072e4c28a7d3b84","target":"record","created_at":"2026-05-18T00:07:43Z","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":"00c905ad9318091c70d723f318849f4dbd8e15c130066a71df08fe07317e89c4","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2017-08-26T15:30:57Z","title_canon_sha256":"a8a4f4275357559d2c6d8e6c8e98ed2e58bfb5dd991a45751e4e0a06e284032d"},"schema_version":"1.0","source":{"id":"1708.07986","kind":"arxiv","version":2}},"canonical_sha256":"e14e9089b27e597fa69e44370309424fa4d36b978023f62717480ee39140f02f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e14e9089b27e597fa69e44370309424fa4d36b978023f62717480ee39140f02f","first_computed_at":"2026-05-18T00:07:43.717886Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:07:43.717886Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"laG1zXxiqn9KMP5Lnr0jxfm9gcFBJy4jVixGy/ih/m9adJLqIPuybu+6X1oZkl9K6LufwM65SELRowkSUj2aBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:07:43.718558Z","signed_message":"canonical_sha256_bytes"},"source_id":"1708.07986","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d93b875e3fcb40815dbaa6b0d3588952404b512479beb3593072e4c28a7d3b84","sha256:5b7520f29932bd5e213cefb3eb178fe1c869d821f8d582bd5baedda65e1bb50b"],"state_sha256":"7a1c6088f9c17eb7a6a661c07eddf599d58b31915be53a86241898cd7177ef6a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ALO15AdI8m9VCYBCwfX8+xOaWzz7JxxKVYmaRIka6vTjwLEo+L8Nc+K9oZbR+xuH1WKIUtshQ7F6WH/fTvr3CA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T03:10:55.607641Z","bundle_sha256":"bd1ae24dd02631eedf76884a934a0a9467f8f3ea8e1fcc6053374ef204876ea8"}}