{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,10]],"date-time":"2026-10-10T05:45:47Z","timestamp":1791611147830,"version":"4.3.4"},"reference-count":32,"publisher":"Oxford University Press (OUP)","issue":"5","license":[{"start":{"date-parts":[[2014,11,7]],"date-time":"2014-11-07T00:00:00Z","timestamp":1415318400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2015,11,1]]},"abstract":"<jats:title>Summary<\/jats:title><jats:p>It is in general challenging to provide confidence intervals for individual variables in high dimensional regression without making strict or unverifiable assumptions on the design matrix. We show here that a \u2018group bound\u2019 confidence interval can be derived without making any assumptions on the design matrix. The lower bound for the regression coefficient of individual variables can be derived via linear programming. The idea also generalizes naturally to groups of variables, where we can derive a one-sided confidence interval for the joint effect of a group. Although the confidence intervals of individual variables are by the nature of the problem often very wide, it is shown to be possible to detect the contribution of groups of highly correlated predictor variables even when no variable individually shows a significant effect. The assumptions that are necessary to detect the effect of groups of variables are shown to be weaker than the weakest known assumptions that are necessary to detect the effect of individual variables.<\/jats:p>","DOI":"10.1111\/rssb.12094","type":"journal-article","created":{"date-parts":[[2014,11,7]],"date-time":"2014-11-07T07:51:55Z","timestamp":1415346715000},"page":"923-945","source":"Crossref","is-referenced-by-count":28,"title":["Group Bound: Confidence Intervals for Groups of Variables in Sparse High Dimensional Regression Without Assumptions on the Design"],"prefix":"10.1093","volume":"77","author":[{"given":"Nicolai","family":"Meinshausen","sequence":"first","affiliation":[{"name":"Eidgen\u00f6ssiche Technische Hochschule Z\u00fcrich \u00a0 Switzerland"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2014,11,7]]},"reference":[{"key":"2023021709295808500_rssb12094-cit-0001","doi-asserted-by":"crossref","first-page":"1705","DOI":"10.1214\/08-AOS620","article-title":"Simultaneous analysis of Lasso and Dantzig selector","volume":"37","author":"Bickel","year":"2009","journal-title":"Ann. 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