{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,9]],"date-time":"2026-10-09T06:11:59Z","timestamp":1791526319687,"version":"4.3.4"},"reference-count":25,"publisher":"Oxford University Press (OUP)","issue":"2","license":[{"start":{"date-parts":[[2016,5,5]],"date-time":"2016-05-05T00:00:00Z","timestamp":1462406400000},"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":[[2017,3,1]]},"abstract":"<jats:title>Summary<\/jats:title><jats:p>Sparse regression techniques have been popular in recent years because of their ability in handling high dimensional data with built-in variable selection. The lasso is perhaps one of the most well-known examples. Despite intensive work in this direction, how to provide valid inference for sparse regularized methods remains a challenging statistical problem. We take a unique point of view of this problem and propose to make use of stochastic variational inequality techniques in optimization to derive confidence intervals and regions for the lasso. Some theoretical properties of the procedure are obtained. Both simulated and real data examples are used to demonstrate the performance of the method.<\/jats:p>","DOI":"10.1111\/rssb.12184","type":"journal-article","created":{"date-parts":[[2016,5,5]],"date-time":"2016-05-05T05:47:05Z","timestamp":1462427225000},"page":"589-611","source":"Crossref","is-referenced-by-count":24,"title":["Confidence Intervals and Regions for the Lasso by Using Stochastic Variational Inequality Techniques in Optimization"],"prefix":"10.1093","volume":"79","author":[{"given":"Shu","family":"Lu","sequence":"first","affiliation":[{"name":"University of North Carolina at Chapel Hill \u00a0 USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yufeng","family":"Liu","sequence":"additional","affiliation":[{"name":"University of North Carolina at Chapel Hill \u00a0 USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Liang","family":"Yin","sequence":"additional","affiliation":[{"name":"University of North Carolina at Chapel Hill \u00a0 USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Kai","family":"Zhang","sequence":"additional","affiliation":[{"name":"University of North Carolina at Chapel Hill \u00a0 USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2016,5,5]]},"reference":[{"key":"2023021709340974500_rssb12184-cit-0001","doi-asserted-by":"crossref","first-page":"802","DOI":"10.1214\/12-AOS1077","article-title":"Valid post-selection inference","volume":"41","author":"Berk","year":"2013","journal-title":"Ann. 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