{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:LAWRNU5TZJTMJ6OAT6OKTWGXIW","short_pith_number":"pith:LAWRNU5T","schema_version":"1.0","canonical_sha256":"582d16d3b3ca66c4f9c09f9ca9d8d745a467a2c5584a6a9d15b480a37e6c3340","source":{"kind":"arxiv","id":"1906.04280","version":1},"attestation_state":"computed","paper":{"title":"Mean estimation and regression under heavy-tailed distributions--a survey","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","stat.ML","stat.TH"],"primary_cat":"math.ST","authors_text":"Gabor Lugosi, Shahar Mendelson","submitted_at":"2019-06-10T21:25:55Z","abstract_excerpt":"We survey some of the recent advances in mean estimation and regression function estimation. In particular, we describe sub-Gaussian mean estimators for possibly heavy-tailed data both in the univariate and multivariate settings. We focus on estimators based on median-of-means techniques but other methods such as the trimmed mean and Catoni's estimator are also reviewed. We give detailed proofs for the cornerstone results. We dedicate a section on statistical learning problems--in particular, regression function estimation--in the presence of possibly heavy-tailed data."},"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":"1906.04280","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2019-06-10T21:25:55Z","cross_cats_sorted":["cs.LG","stat.ML","stat.TH"],"title_canon_sha256":"322f84f3f0edbe31452e853ba7867e95f005b85c1be3389807409d730641e231","abstract_canon_sha256":"efd8b247d9f5e16e2cc5798efb13039ac6788c321170802bfe336bdc94aeb576"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:43:39.738497Z","signature_b64":"h6Q4cD914KWw6fz1Fu/KXP6sHhuFGCIv/y+pbd2WT9WmKPBOwGw1SQHp8cjZ3VCqoF0YJ7LXViv4SCW/zWm4Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"582d16d3b3ca66c4f9c09f9ca9d8d745a467a2c5584a6a9d15b480a37e6c3340","last_reissued_at":"2026-05-17T23:43:39.738067Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:43:39.738067Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Mean estimation and regression under heavy-tailed distributions--a survey","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","stat.ML","stat.TH"],"primary_cat":"math.ST","authors_text":"Gabor Lugosi, Shahar Mendelson","submitted_at":"2019-06-10T21:25:55Z","abstract_excerpt":"We survey some of the recent advances in mean estimation and regression function estimation. In particular, we describe sub-Gaussian mean estimators for possibly heavy-tailed data both in the univariate and multivariate settings. We focus on estimators based on median-of-means techniques but other methods such as the trimmed mean and Catoni's estimator are also reviewed. We give detailed proofs for the cornerstone results. We dedicate a section on statistical learning problems--in particular, regression function estimation--in the presence of possibly heavy-tailed data."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.04280","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":"1906.04280","created_at":"2026-05-17T23:43:39.738130+00:00"},{"alias_kind":"arxiv_version","alias_value":"1906.04280v1","created_at":"2026-05-17T23:43:39.738130+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.04280","created_at":"2026-05-17T23:43:39.738130+00:00"},{"alias_kind":"pith_short_12","alias_value":"LAWRNU5TZJTM","created_at":"2026-05-18T12:33:21.387695+00:00"},{"alias_kind":"pith_short_16","alias_value":"LAWRNU5TZJTMJ6OA","created_at":"2026-05-18T12:33:21.387695+00:00"},{"alias_kind":"pith_short_8","alias_value":"LAWRNU5T","created_at":"2026-05-18T12:33:21.387695+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/LAWRNU5TZJTMJ6OAT6OKTWGXIW","json":"https://pith.science/pith/LAWRNU5TZJTMJ6OAT6OKTWGXIW.json","graph_json":"https://pith.science/api/pith-number/LAWRNU5TZJTMJ6OAT6OKTWGXIW/graph.json","events_json":"https://pith.science/api/pith-number/LAWRNU5TZJTMJ6OAT6OKTWGXIW/events.json","paper":"https://pith.science/paper/LAWRNU5T"},"agent_actions":{"view_html":"https://pith.science/pith/LAWRNU5TZJTMJ6OAT6OKTWGXIW","download_json":"https://pith.science/pith/LAWRNU5TZJTMJ6OAT6OKTWGXIW.json","view_paper":"https://pith.science/paper/LAWRNU5T","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1906.04280&json=true","fetch_graph":"https://pith.science/api/pith-number/LAWRNU5TZJTMJ6OAT6OKTWGXIW/graph.json","fetch_events":"https://pith.science/api/pith-number/LAWRNU5TZJTMJ6OAT6OKTWGXIW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LAWRNU5TZJTMJ6OAT6OKTWGXIW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LAWRNU5TZJTMJ6OAT6OKTWGXIW/action/storage_attestation","attest_author":"https://pith.science/pith/LAWRNU5TZJTMJ6OAT6OKTWGXIW/action/author_attestation","sign_citation":"https://pith.science/pith/LAWRNU5TZJTMJ6OAT6OKTWGXIW/action/citation_signature","submit_replication":"https://pith.science/pith/LAWRNU5TZJTMJ6OAT6OKTWGXIW/action/replication_record"}},"created_at":"2026-05-17T23:43:39.738130+00:00","updated_at":"2026-05-17T23:43:39.738130+00:00"}