{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,6]],"date-time":"2026-10-06T21:53:05Z","timestamp":1791323585222,"version":"4.3.1"},"reference-count":77,"publisher":"Institute of Mathematical Statistics","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Ann. Statist."],"published-print":{"date-parts":[[2026,4,1]]},"abstract":"We study the classical problem of predicting an outcome variable, Y, using a linear combination of a d-dimensional covariate vector, X. We are interested in linear predictors whose coefficients solve inf\u03b2\u2208Rd(EPn[|Y\u2212X\u22a4\u03b2|r])1\/r+\u03b4\u03c1(\u03b2), where \u03b4>0 is a regularization parameter, \u03c1:Rd\u2192R+ is a convex penalty function, Pn is the empirical distribution of the data and r\u22651. Our main contribution is a new bound on the out-of-distribution prediction error of such estimators. The new bound is obtained by combining three new sets of results. First, we provide conditions under which linear predictors based on these estimators solve a distributionally robust optimization problem: they minimize the worst-case prediction error over distributions that are close to each other in a type of max-sliced Wasserstein metric. Second, we provide a detailed finite-sample and asymptotic analysis of the statistical properties of the balls of distributions over which the worst-case prediction error is analyzed. Third, we present an oracle recommendation for the choice of regularization parameter, \u03b4, that guarantees good out-of-distribution prediction error.<\/jats:p>","DOI":"10.1214\/25-aos2599","type":"journal-article","created":{"date-parts":[[2026,4,2]],"date-time":"2026-04-02T13:05:20Z","timestamp":1775135120000},"page":"1006-1027","source":"Crossref","is-referenced-by-count":0,"title":["The distributionally robust prediction error of the LASSO and related estimators"],"prefix":"10.1214","volume":"54","author":[{"given":"Jos\u00e9 Luis","family":"Montiel Olea","sequence":"first","affiliation":[{"name":"Department of Economics, Cornell University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Cynthia","family":"Rush","sequence":"additional","affiliation":[{"name":"Department of Statistics, Columbia University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Amilcar","family":"Velez","sequence":"additional","affiliation":[{"name":"Department of Economics, Cornell University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Johannes","family":"Wiesel","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Copenhagen"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"108","reference":[{"key":"42","doi-asserted-by":"publisher","unstructured":"KPOTUFE, S.<\/small> and MARTINET, G.<\/small> (2021). 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