{"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"}