{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:CJDPZWZG2IA3GNDXRNM4BX26MU","short_pith_number":"pith:CJDPZWZG","schema_version":"1.0","canonical_sha256":"1246fcdb26d201b334778b59c0df5e651e908cfedb2f8f78fa47317a450778ad","source":{"kind":"arxiv","id":"1803.09713","version":1},"attestation_state":"computed","paper":{"title":"Robust principal components for irregularly spaced longitudinal data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.ME","authors_text":"Ricardo A. Maronna (University of La Plata, University of Buenos Aires)","submitted_at":"2018-03-26T17:01:52Z","abstract_excerpt":"Consider longitudinal data $x_{ij},$ with $i=1,...,n$ and $j=1,...,p_{i},$ where $x_{ij}$ is the $j-$th observation of the random function $X_{i}\\left( .\\right) $ observed at time $t_{j}.$ The goal of this paper is to develop a parsimonious representation of the data by a linear combination of a set of $q$ smooth functions $H_{k}\\left( .\\right) $ ($k=1,..,q)$ in the sense that $x_{ij}\\approx\\mu_{j}+\\sum_{k=1}^{q}\\beta_{ki}H_{k}\\left( t_{j}\\right) ,$ such that it fulfills three goals: it is resistant to atypical $X_{i}$'s ('case contamination'), it is resistant to isolated gross errors at some "},"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":"1803.09713","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2018-03-26T17:01:52Z","cross_cats_sorted":[],"title_canon_sha256":"ba3e3ebcdb028bc8922c515422760062b6ab635bf94bcb6f87b3a10df581f54c","abstract_canon_sha256":"dfa03c34d7db87dba505cb2bb86a8330163d21b376dda6d8dc61fcb866c34584"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:20:10.622713Z","signature_b64":"BY6E3sKS4Q+dr3puB9Lcpi5zVkBPwEpWmwLQJx84o7neT8jcMvsf6EqewiOmFwTd5ezzerYHveJ76kO4eI+/Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1246fcdb26d201b334778b59c0df5e651e908cfedb2f8f78fa47317a450778ad","last_reissued_at":"2026-05-18T00:20:10.622023Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:20:10.622023Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Robust principal components for irregularly spaced longitudinal data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.ME","authors_text":"Ricardo A. Maronna (University of La Plata, University of Buenos Aires)","submitted_at":"2018-03-26T17:01:52Z","abstract_excerpt":"Consider longitudinal data $x_{ij},$ with $i=1,...,n$ and $j=1,...,p_{i},$ where $x_{ij}$ is the $j-$th observation of the random function $X_{i}\\left( .\\right) $ observed at time $t_{j}.$ The goal of this paper is to develop a parsimonious representation of the data by a linear combination of a set of $q$ smooth functions $H_{k}\\left( .\\right) $ ($k=1,..,q)$ in the sense that $x_{ij}\\approx\\mu_{j}+\\sum_{k=1}^{q}\\beta_{ki}H_{k}\\left( t_{j}\\right) ,$ such that it fulfills three goals: it is resistant to atypical $X_{i}$'s ('case contamination'), it is resistant to isolated gross errors at some "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.09713","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":"1803.09713","created_at":"2026-05-18T00:20:10.622127+00:00"},{"alias_kind":"arxiv_version","alias_value":"1803.09713v1","created_at":"2026-05-18T00:20:10.622127+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.09713","created_at":"2026-05-18T00:20:10.622127+00:00"},{"alias_kind":"pith_short_12","alias_value":"CJDPZWZG2IA3","created_at":"2026-05-18T12:32:16.446611+00:00"},{"alias_kind":"pith_short_16","alias_value":"CJDPZWZG2IA3GNDX","created_at":"2026-05-18T12:32:16.446611+00:00"},{"alias_kind":"pith_short_8","alias_value":"CJDPZWZG","created_at":"2026-05-18T12:32:16.446611+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/CJDPZWZG2IA3GNDXRNM4BX26MU","json":"https://pith.science/pith/CJDPZWZG2IA3GNDXRNM4BX26MU.json","graph_json":"https://pith.science/api/pith-number/CJDPZWZG2IA3GNDXRNM4BX26MU/graph.json","events_json":"https://pith.science/api/pith-number/CJDPZWZG2IA3GNDXRNM4BX26MU/events.json","paper":"https://pith.science/paper/CJDPZWZG"},"agent_actions":{"view_html":"https://pith.science/pith/CJDPZWZG2IA3GNDXRNM4BX26MU","download_json":"https://pith.science/pith/CJDPZWZG2IA3GNDXRNM4BX26MU.json","view_paper":"https://pith.science/paper/CJDPZWZG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1803.09713&json=true","fetch_graph":"https://pith.science/api/pith-number/CJDPZWZG2IA3GNDXRNM4BX26MU/graph.json","fetch_events":"https://pith.science/api/pith-number/CJDPZWZG2IA3GNDXRNM4BX26MU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CJDPZWZG2IA3GNDXRNM4BX26MU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CJDPZWZG2IA3GNDXRNM4BX26MU/action/storage_attestation","attest_author":"https://pith.science/pith/CJDPZWZG2IA3GNDXRNM4BX26MU/action/author_attestation","sign_citation":"https://pith.science/pith/CJDPZWZG2IA3GNDXRNM4BX26MU/action/citation_signature","submit_replication":"https://pith.science/pith/CJDPZWZG2IA3GNDXRNM4BX26MU/action/replication_record"}},"created_at":"2026-05-18T00:20:10.622127+00:00","updated_at":"2026-05-18T00:20:10.622127+00:00"}