{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:XXXLJVJKQ2VTFVNFJBKQIPR73P","short_pith_number":"pith:XXXLJVJK","schema_version":"1.0","canonical_sha256":"bdeeb4d52a86ab32d5a54855043e3fdbeec3ba169115dd41cb8947d4e343eae0","source":{"kind":"arxiv","id":"1310.8244","version":4},"attestation_state":"computed","paper":{"title":"Rates of convergence in conditional covariance matrix with nonparametric entries estimation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.ME","authors_text":"Clement Marteau, Jean-Michel Loubes, Maikol Sol\\'is","submitted_at":"2013-10-30T17:50:37Z","abstract_excerpt":"Let $X\\in \\mathbb{R}^p$ and $Y\\in \\mathbb{R}$ be two random variables. We estimate the conditional covariance matrix $\\mathrm{Cov}\\left(\\mathrm{E}\\left[\\boldsymbol{X}\\vert Y\\right]\\right)$ applying a plug-in kernel-based algorithm to its entries. Next, we investigate the estimators rate of convergence under smoothness hypotheses on the density function of $(\\boldsymbol{X},Y)$. In a high-dimensional context, we improve the consistency the whole matrix estimator by providing a decreasing structure over the $\\mathrm{Cov}\\left(\\mathrm{E}\\left[\\boldsymbol{X}\\vert Y\\right]\\right)$ entries. We illust"},"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":"1310.8244","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2013-10-30T17:50:37Z","cross_cats_sorted":[],"title_canon_sha256":"48b3b59a4ddb716c451e0b42f62891ce81d9f6c41b3c4db7055b23db28b3d0a8","abstract_canon_sha256":"8adf7fa8541df1f8e52ef275b96912257000056beb8a0d7906b82a1588ebd915"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:23:57.627242Z","signature_b64":"FYwvWCoy3Smcudu3S4ta1uBr5n03A4le1X/07Yr/Ks6lokbkFNFJ7Q+uhAcZW0iEyFX2aWg4IlBhnKirn3F6Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bdeeb4d52a86ab32d5a54855043e3fdbeec3ba169115dd41cb8947d4e343eae0","last_reissued_at":"2026-05-18T00:23:57.626692Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:23:57.626692Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Rates of convergence in conditional covariance matrix with nonparametric entries estimation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.ME","authors_text":"Clement Marteau, Jean-Michel Loubes, Maikol Sol\\'is","submitted_at":"2013-10-30T17:50:37Z","abstract_excerpt":"Let $X\\in \\mathbb{R}^p$ and $Y\\in \\mathbb{R}$ be two random variables. We estimate the conditional covariance matrix $\\mathrm{Cov}\\left(\\mathrm{E}\\left[\\boldsymbol{X}\\vert Y\\right]\\right)$ applying a plug-in kernel-based algorithm to its entries. Next, we investigate the estimators rate of convergence under smoothness hypotheses on the density function of $(\\boldsymbol{X},Y)$. In a high-dimensional context, we improve the consistency the whole matrix estimator by providing a decreasing structure over the $\\mathrm{Cov}\\left(\\mathrm{E}\\left[\\boldsymbol{X}\\vert Y\\right]\\right)$ entries. We illust"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.8244","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":"1310.8244","created_at":"2026-05-18T00:23:57.626767+00:00"},{"alias_kind":"arxiv_version","alias_value":"1310.8244v4","created_at":"2026-05-18T00:23:57.626767+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.8244","created_at":"2026-05-18T00:23:57.626767+00:00"},{"alias_kind":"pith_short_12","alias_value":"XXXLJVJKQ2VT","created_at":"2026-05-18T12:28:06.772260+00:00"},{"alias_kind":"pith_short_16","alias_value":"XXXLJVJKQ2VTFVNF","created_at":"2026-05-18T12:28:06.772260+00:00"},{"alias_kind":"pith_short_8","alias_value":"XXXLJVJK","created_at":"2026-05-18T12:28:06.772260+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/XXXLJVJKQ2VTFVNFJBKQIPR73P","json":"https://pith.science/pith/XXXLJVJKQ2VTFVNFJBKQIPR73P.json","graph_json":"https://pith.science/api/pith-number/XXXLJVJKQ2VTFVNFJBKQIPR73P/graph.json","events_json":"https://pith.science/api/pith-number/XXXLJVJKQ2VTFVNFJBKQIPR73P/events.json","paper":"https://pith.science/paper/XXXLJVJK"},"agent_actions":{"view_html":"https://pith.science/pith/XXXLJVJKQ2VTFVNFJBKQIPR73P","download_json":"https://pith.science/pith/XXXLJVJKQ2VTFVNFJBKQIPR73P.json","view_paper":"https://pith.science/paper/XXXLJVJK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1310.8244&json=true","fetch_graph":"https://pith.science/api/pith-number/XXXLJVJKQ2VTFVNFJBKQIPR73P/graph.json","fetch_events":"https://pith.science/api/pith-number/XXXLJVJKQ2VTFVNFJBKQIPR73P/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XXXLJVJKQ2VTFVNFJBKQIPR73P/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XXXLJVJKQ2VTFVNFJBKQIPR73P/action/storage_attestation","attest_author":"https://pith.science/pith/XXXLJVJKQ2VTFVNFJBKQIPR73P/action/author_attestation","sign_citation":"https://pith.science/pith/XXXLJVJKQ2VTFVNFJBKQIPR73P/action/citation_signature","submit_replication":"https://pith.science/pith/XXXLJVJKQ2VTFVNFJBKQIPR73P/action/replication_record"}},"created_at":"2026-05-18T00:23:57.626767+00:00","updated_at":"2026-05-18T00:23:57.626767+00:00"}