{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:CJMJ4A2ED2XLBNQ52CGBRSMLLN","short_pith_number":"pith:CJMJ4A2E","schema_version":"1.0","canonical_sha256":"12589e03441eaeb0b61dd08c18c98b5b4ab4ea12afee8ca873ac785c740cf76f","source":{"kind":"arxiv","id":"1903.10914","version":1},"attestation_state":"computed","paper":{"title":"Estimation of a regular conditional functional by conditional U-statistics regression","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Alexis Derumigny","submitted_at":"2019-03-26T14:18:51Z","abstract_excerpt":"U-statistics constitute a large class of estimators, generalizing the empirical mean of a random variable $X$ to sums over every $k$-tuple of distinct observations of $X$. They may be used to estimate a regular functional $\\theta(P_{X})$ of the law of $X$. When a vector of covariates $Z$ is available, a conditional U-statistic may describe the effect of $z$ on the conditional law of $X$ given $Z=z$, by estimating a regular conditional functional $\\theta(P_{X|Z=\\cdot})$. We prove concentration inequalities for conditional U-statistics. Assuming a parametric model of the conditional functional o"},"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":"1903.10914","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2019-03-26T14:18:51Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"7f3bd8bcd7cfbd3324b20c87519265ada33b3a47be0106841bf2b6de5d0941ff","abstract_canon_sha256":"3aba5d6d2a8af9d2e39c127b8d6407b587de1296434b17bec229bef4ee77a916"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:50:17.250368Z","signature_b64":"ILEbiWkHS/g9dAJsDbi0ECAd9m5BVK6LnPMQy3Ti/A8lqJ6ee2LKkX1Gx0uduBvYPZzWrjUllTqfznpof9OFAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"12589e03441eaeb0b61dd08c18c98b5b4ab4ea12afee8ca873ac785c740cf76f","last_reissued_at":"2026-05-17T23:50:17.249773Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:50:17.249773Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Estimation of a regular conditional functional by conditional U-statistics regression","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Alexis Derumigny","submitted_at":"2019-03-26T14:18:51Z","abstract_excerpt":"U-statistics constitute a large class of estimators, generalizing the empirical mean of a random variable $X$ to sums over every $k$-tuple of distinct observations of $X$. They may be used to estimate a regular functional $\\theta(P_{X})$ of the law of $X$. When a vector of covariates $Z$ is available, a conditional U-statistic may describe the effect of $z$ on the conditional law of $X$ given $Z=z$, by estimating a regular conditional functional $\\theta(P_{X|Z=\\cdot})$. We prove concentration inequalities for conditional U-statistics. Assuming a parametric model of the conditional functional o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.10914","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":"1903.10914","created_at":"2026-05-17T23:50:17.249839+00:00"},{"alias_kind":"arxiv_version","alias_value":"1903.10914v1","created_at":"2026-05-17T23:50:17.249839+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.10914","created_at":"2026-05-17T23:50:17.249839+00:00"},{"alias_kind":"pith_short_12","alias_value":"CJMJ4A2ED2XL","created_at":"2026-05-18T12:33:15.570797+00:00"},{"alias_kind":"pith_short_16","alias_value":"CJMJ4A2ED2XLBNQ5","created_at":"2026-05-18T12:33:15.570797+00:00"},{"alias_kind":"pith_short_8","alias_value":"CJMJ4A2E","created_at":"2026-05-18T12:33:15.570797+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/CJMJ4A2ED2XLBNQ52CGBRSMLLN","json":"https://pith.science/pith/CJMJ4A2ED2XLBNQ52CGBRSMLLN.json","graph_json":"https://pith.science/api/pith-number/CJMJ4A2ED2XLBNQ52CGBRSMLLN/graph.json","events_json":"https://pith.science/api/pith-number/CJMJ4A2ED2XLBNQ52CGBRSMLLN/events.json","paper":"https://pith.science/paper/CJMJ4A2E"},"agent_actions":{"view_html":"https://pith.science/pith/CJMJ4A2ED2XLBNQ52CGBRSMLLN","download_json":"https://pith.science/pith/CJMJ4A2ED2XLBNQ52CGBRSMLLN.json","view_paper":"https://pith.science/paper/CJMJ4A2E","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1903.10914&json=true","fetch_graph":"https://pith.science/api/pith-number/CJMJ4A2ED2XLBNQ52CGBRSMLLN/graph.json","fetch_events":"https://pith.science/api/pith-number/CJMJ4A2ED2XLBNQ52CGBRSMLLN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CJMJ4A2ED2XLBNQ52CGBRSMLLN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CJMJ4A2ED2XLBNQ52CGBRSMLLN/action/storage_attestation","attest_author":"https://pith.science/pith/CJMJ4A2ED2XLBNQ52CGBRSMLLN/action/author_attestation","sign_citation":"https://pith.science/pith/CJMJ4A2ED2XLBNQ52CGBRSMLLN/action/citation_signature","submit_replication":"https://pith.science/pith/CJMJ4A2ED2XLBNQ52CGBRSMLLN/action/replication_record"}},"created_at":"2026-05-17T23:50:17.249839+00:00","updated_at":"2026-05-17T23:50:17.249839+00:00"}