{"paper":{"title":"The out-of-sample prediction error of the square-root-LASSO and related estimators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC","stat.TH"],"primary_cat":"math.ST","authors_text":"Amilcar Velez, Cynthia Rush, Johannes Wiesel, Jos\\'e Luis Montiel Olea","submitted_at":"2022-11-14T18:31:10Z","abstract_excerpt":"We study the classical problem of predicting an outcome variable, $Y$, using a linear combination of a $d$-dimensional covariate vector, $\\mathbf{X}$. We are interested in linear predictors whose coefficients solve: % \\begin{align*} \\inf_{\\boldsymbol{\\beta} \\in \\mathbb{R}^d} \\left( \\mathbb{E}_{\\mathbb{P}_n} \\left[ \\left(Y-\\mathbf{X}^{\\top}\\beta \\right)^r \\right] \\right)^{1/r} +\\delta \\, \\rho\\left(\\boldsymbol{\\beta}\\right), \\end{align*} where $\\delta>0$ is a regularization parameter, $\\rho:\\mathbb{R}^d\\to \\mathbb{R}_+$ is a convex penalty function, $\\mathbb{P}_n$ is the empirical distribution o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2211.07608","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2211.07608/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}