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This may result in biased prediction, especially when weak signals outnumber strong signals. This paper aims to incorporate weak signals in variable selection, estimation, and prediction. We propose a two\u2010stage procedure, consisting of variable selection and postselection estimation. The variable selection stage involves a covariance\u2010insured screening for detecting weak signals, whereas the postselection estimation stage involves a shrinkage estimator for jointly estimating strong and weak signals selected from the first stage. We term the proposed method as the covariance\u2010insured screening\u2010based postselection shrinkage estimator. We establish asymptotic properties for the proposed method and show, via simulations, that incorporating weak signals can improve estimation and prediction performance. We apply the proposed method to predict the annual gross domestic product rates based on various socioeconomic indicators for 82\u00a0countries.<\/jats:p>","DOI":"10.1002\/asmb.2340","type":"journal-article","created":{"date-parts":[[2018,5,25]],"date-time":"2018-05-25T08:59:48Z","timestamp":1527238788000},"page":"283-298","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":16,"title":["Weak signals in high\u2010dimensional regression: Detection, estimation and prediction"],"prefix":"10.1002","volume":"35","author":[{"given":"Yanming","family":"Li","sequence":"first","affiliation":[{"name":"Department of Biostatistics University of Michigan Ann Arbor MI USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hyokyoung G.","family":"Hong","sequence":"additional","affiliation":[{"name":"Department of Statistics and Probability Michigan State University East Lansing MI USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"S. Ejaz","family":"Ahmed","sequence":"additional","affiliation":[{"name":"Department of Mathematics &amp; Statistics Brock University St. Catharines ON Canada"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yi","family":"Li","sequence":"additional","affiliation":[{"name":"Department of Biostatistics University of Michigan Ann Arbor MI USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2018,5,25]]},"reference":[{"issue":"1","key":"e_1_2_7_2_1","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1111\/j.2517-6161.1996.tb02080.x","article-title":"Regression shrinkage and selection via the Lasso","volume":"58","author":"Tibshirani R","year":"1996","journal-title":"J Royal Stat Soc Ser B"},{"key":"e_1_2_7_3_1","doi-asserted-by":"publisher","DOI":"10.1198\/016214506000000735"},{"key":"e_1_2_7_4_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-9868.2005.00532.x"},{"key":"e_1_2_7_5_1","doi-asserted-by":"publisher","DOI":"10.1198\/016214501753382273"},{"key":"e_1_2_7_6_1","doi-asserted-by":"publisher","DOI":"10.1214\/09-AOS729"},{"key":"e_1_2_7_7_1","doi-asserted-by":"publisher","DOI":"10.1111\/rssb.12026"},{"key":"e_1_2_7_8_1","first-page":"781","article-title":"Exact covariance thresholding into connected components for large\u2010scale graphical Lasso","volume":"13","author":"Mazumder R","year":"2012","journal-title":"J Mach Learn Res"},{"key":"e_1_2_7_9_1","doi-asserted-by":"publisher","DOI":"10.1214\/08-AOS600"},{"key":"e_1_2_7_10_1","doi-asserted-by":"publisher","DOI":"10.1214\/11-AOS944"},{"key":"e_1_2_7_11_1","doi-asserted-by":"publisher","DOI":"10.1214\/10-AOS870"},{"key":"e_1_2_7_12_1","doi-asserted-by":"publisher","DOI":"10.1002\/asmb.2193"},{"key":"e_1_2_7_13_1","doi-asserted-by":"publisher","DOI":"10.1214\/07-AOS520"},{"key":"e_1_2_7_14_1","unstructured":"BarroR LeeJ.Data set for a panel of 139 countries NBER.1994.http:\/\/admin.nber.org\/pub\/barro.lee\/"},{"key":"e_1_2_7_15_1","doi-asserted-by":"publisher","DOI":"10.1038\/ng.f.136"},{"key":"e_1_2_7_16_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.ajhg.2008.06.024"},{"key":"e_1_2_7_17_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.ajhg.2011.05.029"},{"key":"e_1_2_7_18_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jspi.2013.05.019"},{"key":"e_1_2_7_19_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jspi.2013.05.022"},{"key":"e_1_2_7_20_1","volume-title":"Computer Vision","author":"Shapiro L","year":"2002"}],"container-title":["Applied Stochastic Models in Business and Industry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fasmb.2340","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/asmb.2340","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/full-xml\/10.1002\/asmb.2340","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/asmb.2340","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,7,7]],"date-time":"2024-07-07T00:22:47Z","timestamp":1720311767000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/asmb.2340"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,5,25]]},"references-count":19,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2019,3]]}},"alternative-id":["10.1002\/asmb.2340"],"URL":"https:\/\/doi.org\/10.1002\/asmb.2340","archive":["Portico"],"relation":{},"ISSN":["1524-1904","1526-4025"],"issn-type":[{"value":"1524-1904","type":"print"},{"value":"1526-4025","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,5,25]]},"assertion":[{"value":"2017-10-13","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2018-04-25","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2018-05-25","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}