{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,9]],"date-time":"2026-03-09T01:46:07Z","timestamp":1773020767940,"version":"3.50.1"},"reference-count":38,"publisher":"Oxford University Press (OUP)","issue":"9","license":[{"start":{"date-parts":[[2024,9,10]],"date-time":"2024-09-10T00:00:00Z","timestamp":1725926400000},"content-version":"vor","delay-in-days":9,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12201260"],"award-info":[{"award-number":["12201260"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002858","name":"China Postdoctoral Science Foundation","doi-asserted-by":"publisher","award":["2022M711425"],"award-info":[{"award-number":["2022M711425"]}],"id":[{"id":"10.13039\/501100002858","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2024,9,2]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:sec>\n                  <jats:title>Motivation<\/jats:title>\n                  <jats:p>The functions of genes in networks are typically correlated due to their functional connectivity. Variable selection methods have been developed to select important genes associated with a trait while incorporating network graphical information. However, no method has been proposed to quantify the uncertainty of individual genes under such settings.<\/jats:p>\n               <\/jats:sec>\n               <jats:sec>\n                  <jats:title>Results<\/jats:title>\n                  <jats:p>In this paper, we construct confidence intervals (CIs) and provide P-values for parameters of a high-dimensional linear model incorporating graphical structures where the number of variables p diverges with the number of observations. For combining the graphical information, we propose a graph-constrained desparsified LASSO (least absolute shrinkage and selection operator) (GCDL) estimator, which reduces dramatically the influence of high correlation of predictors and enjoys the advantage of faster computation and higher accuracy compared with the desparsified LASSO. Theoretical results show that the GCDL estimator achieves asymptotic normality. The asymptotic property of the uniform convergence is established, with which an explicit expression of the uniform CI can be derived. Extensive numerical results indicate that the GCDL estimator and its (uniform) CI perform well even when predictors are highly correlated.<\/jats:p>\n               <\/jats:sec>\n               <jats:sec>\n                  <jats:title>Availability and implementation<\/jats:title>\n                  <jats:p>An R package implementing the proposed method is available at https:\/\/github.com\/XiaoZhangryy\/gcdl.<\/jats:p>\n               <\/jats:sec>","DOI":"10.1093\/bioinformatics\/btae541","type":"journal-article","created":{"date-parts":[[2024,9,10]],"date-time":"2024-09-10T14:14:31Z","timestamp":1725977671000},"source":"Crossref","is-referenced-by-count":1,"title":["Uncertainty quantification in high-dimensional linear models incorporating graphical structures with applications to gene set analysis"],"prefix":"10.1093","volume":"40","author":[{"given":"Xiangyong","family":"Tan","sequence":"first","affiliation":[{"name":"School of Statistics and Data Science, Jiangxi University of Finance and Economics , Nanchang 330013,","place":["China"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiao","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Data Science, The Chinese University of Hong Kong , Shenzhen 518172,","place":["China"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8099-1753","authenticated-orcid":false,"given":"Yuehua","family":"Cui","sequence":"additional","affiliation":[{"name":"Department of Statistics and Probability, Michigan State University , East Lansing, MI 48824,","place":["United States"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3829-1715","authenticated-orcid":false,"given":"Xu","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Statistics and Management, Shanghai University of Finance and Economics , Shanghai 200433,","place":["China"]},{"name":"Yunnan Key Laboratory of Statistical Modeling and Data Analysis, Yunnan University , Kunming 650500,","place":["China"]}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2024,9,10]]},"reference":[{"key":"2024092721062052900_btae541-B1","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1038\/75556","article-title":"Gene ontology: tool for the unification of biology","volume":"25","author":"Ashburner","year":"2000","journal-title":"Nat Genet"},{"key":"2024092721062052900_btae541-B2","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 Stat"},{"key":"2024092721062052900_btae541-B3","doi-asserted-by":"crossref","first-page":"232","DOI":"10.1214\/10-AOAS388","article-title":"Coordinate descent algorithms for nonconvex penalized regression, with applications to biological feature 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