{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:MH32MBHDSCCLM5I2MZRGI26WUJ","short_pith_number":"pith:MH32MBHD","schema_version":"1.0","canonical_sha256":"61f7a604e39084b6751a6662646bd6a27ba298593bc7d7d50a71a4c7d62ef1d0","source":{"kind":"arxiv","id":"1209.6534","version":1},"attestation_state":"computed","paper":{"title":"Model selection and estimation of a component in additive regression","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Xavier Gendre (IMT)","submitted_at":"2012-09-28T14:31:42Z","abstract_excerpt":"Let $Y\\in\\R^n$ be a random vector with mean $s$ and covariance matrix $\\sigma^2P_n\\tra{P_n}$ where $P_n$ is some known $n\\times n$-matrix. We construct a statistical procedure to estimate $s$ as well as under moment condition on $Y$ or Gaussian hypothesis. Both cases are developed for known or unknown $\\sigma^2$. Our approach is free from any prior assumption on $s$ and is based on non-asymptotic model selection methods. Given some linear spaces collection $\\{S_m,\\ m\\in\\M\\}$, we consider, for any $m\\in\\M$, the least-squares estimator $\\hat{s}_m$ of $s$ in $S_m$. Considering a penalty function "},"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":"1209.6534","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2012-09-28T14:31:42Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"48c38d53e38f43d2494495df527136cc115f42cc599ae3eccddc3d838fcc6e1b","abstract_canon_sha256":"7a5335c188eabf2d123f79002423e6cea27b4c6fc08c63e1a9b5769861fbe3c5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:44:25.206663Z","signature_b64":"c9UVdAra/GTRF9iPIqZ9tAnbmpcGvVPI9BqYmfHCkKWXPBwgdz1BPZb/chZCsbKW+6GUKIU7JPwbhGjE100zBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"61f7a604e39084b6751a6662646bd6a27ba298593bc7d7d50a71a4c7d62ef1d0","last_reissued_at":"2026-05-18T03:44:25.206024Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:44:25.206024Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Model selection and estimation of a component in additive regression","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Xavier Gendre (IMT)","submitted_at":"2012-09-28T14:31:42Z","abstract_excerpt":"Let $Y\\in\\R^n$ be a random vector with mean $s$ and covariance matrix $\\sigma^2P_n\\tra{P_n}$ where $P_n$ is some known $n\\times n$-matrix. We construct a statistical procedure to estimate $s$ as well as under moment condition on $Y$ or Gaussian hypothesis. Both cases are developed for known or unknown $\\sigma^2$. Our approach is free from any prior assumption on $s$ and is based on non-asymptotic model selection methods. Given some linear spaces collection $\\{S_m,\\ m\\in\\M\\}$, we consider, for any $m\\in\\M$, the least-squares estimator $\\hat{s}_m$ of $s$ in $S_m$. Considering a penalty function "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.6534","kind":"arxiv","version":1},"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":"1209.6534","created_at":"2026-05-18T03:44:25.206119+00:00"},{"alias_kind":"arxiv_version","alias_value":"1209.6534v1","created_at":"2026-05-18T03:44:25.206119+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.6534","created_at":"2026-05-18T03:44:25.206119+00:00"},{"alias_kind":"pith_short_12","alias_value":"MH32MBHDSCCL","created_at":"2026-05-18T12:27:14.488303+00:00"},{"alias_kind":"pith_short_16","alias_value":"MH32MBHDSCCLM5I2","created_at":"2026-05-18T12:27:14.488303+00:00"},{"alias_kind":"pith_short_8","alias_value":"MH32MBHD","created_at":"2026-05-18T12:27:14.488303+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/MH32MBHDSCCLM5I2MZRGI26WUJ","json":"https://pith.science/pith/MH32MBHDSCCLM5I2MZRGI26WUJ.json","graph_json":"https://pith.science/api/pith-number/MH32MBHDSCCLM5I2MZRGI26WUJ/graph.json","events_json":"https://pith.science/api/pith-number/MH32MBHDSCCLM5I2MZRGI26WUJ/events.json","paper":"https://pith.science/paper/MH32MBHD"},"agent_actions":{"view_html":"https://pith.science/pith/MH32MBHDSCCLM5I2MZRGI26WUJ","download_json":"https://pith.science/pith/MH32MBHDSCCLM5I2MZRGI26WUJ.json","view_paper":"https://pith.science/paper/MH32MBHD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1209.6534&json=true","fetch_graph":"https://pith.science/api/pith-number/MH32MBHDSCCLM5I2MZRGI26WUJ/graph.json","fetch_events":"https://pith.science/api/pith-number/MH32MBHDSCCLM5I2MZRGI26WUJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MH32MBHDSCCLM5I2MZRGI26WUJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MH32MBHDSCCLM5I2MZRGI26WUJ/action/storage_attestation","attest_author":"https://pith.science/pith/MH32MBHDSCCLM5I2MZRGI26WUJ/action/author_attestation","sign_citation":"https://pith.science/pith/MH32MBHDSCCLM5I2MZRGI26WUJ/action/citation_signature","submit_replication":"https://pith.science/pith/MH32MBHDSCCLM5I2MZRGI26WUJ/action/replication_record"}},"created_at":"2026-05-18T03:44:25.206119+00:00","updated_at":"2026-05-18T03:44:25.206119+00:00"}