{"paper":{"title":"Statistical estimation and testing via the sorted L1 norm","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.ST","stat.TH"],"primary_cat":"stat.ME","authors_text":"Emmanuel Candes, Ewout van den Berg, Malgorzata Bogdan, Weijie Su","submitted_at":"2013-10-07T22:31:20Z","abstract_excerpt":"We introduce a novel method for sparse regression and variable selection, which is inspired by modern ideas in multiple testing. Imagine we have observations from the linear model y = X beta + z, then we suggest estimating the regression coefficients by means of a new estimator called SLOPE, which is the solution to minimize 0.5 ||y - Xb\\|_2^2 + lambda_1 |b|_(1) + lambda_2 |b|_(2) + ... + lambda_p |b|_(p); here, lambda_1 >= \\lambda_2 >= ... >= \\lambda_p >= 0 and |b|_(1) >= |b|_(2) >= ... >= |b|_(p) is the order statistic of the magnitudes of b. The regularizer is a sorted L1 norm which penaliz"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.1969","kind":"arxiv","version":2},"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"}