{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,23]],"date-time":"2026-09-23T04:11:49Z","timestamp":1790136709713,"version":"4.0.1"},"reference-count":38,"publisher":"Oxford University Press (OUP)","issue":"1","license":[{"start":{"date-parts":[[2022,4,5]],"date-time":"2022-04-05T00:00:00Z","timestamp":1649116800000},"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":[[2023,2,11]]},"abstract":"<jats:title>Summary<\/jats:title>\n               <jats:p>Generalized linear models often have high-dimensional nuisance parameters, as seen in applications such as testing gene-environment interactions or gene-gene interactions. In these scenarios, it is essential to test the significance of a high-dimensional subvector of the model\u2019s coefficients. Although some existing methods can tackle this problem, they often rely on the bootstrap to approximate the asymptotic distribution of the test statistic, and are thus computationally expensive. Here, we propose a computationally efficient test with a closed-form limiting distribution, which allows the parameter being tested to be either sparse or dense. We show that, under certain regularity conditions, the Type-I error of the proposed method is asymptotically correct, and we establish its power under high-dimensional alternatives. Extensive simulations demonstrate the good performance of the proposed test and its robustness when certain sparsity assumptions are violated. We also apply the proposed method to Chinese famine sample data in order to show its performance when testing the significance of gene-environment interactions.<\/jats:p>","DOI":"10.1093\/biomet\/asac021","type":"journal-article","created":{"date-parts":[[2022,4,5]],"date-time":"2022-04-05T13:46:52Z","timestamp":1649166412000},"page":"83-99","source":"Crossref","is-referenced-by-count":13,"title":["Testing generalized linear models with high-dimensional nuisance parameters"],"prefix":"10.1093","volume":"110","author":[{"given":"Jinsong","family":"Chen","sequence":"first","affiliation":[{"name":"College of Applied Health Sciences, University of Illinois at Chicago , 1919 W Taylor St, Chicago, Illinois 60612, U.S.A"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Quefeng","family":"Li","sequence":"additional","affiliation":[{"name":"Department of Biostatistics, University of North Carolina at Chapel Hill , Chapel Hill, North Carolina 27599, U.S.A"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hua Yun","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Public Health, University of Illinois at Chicago , 2121 W Taylor St, Chicago, Illinois 60612, U.S.A"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2022,4,5]]},"reference":[{"key":"2023021111212296000_B1","doi-asserted-by":"crossref","first-page":"64","DOI":"10.1080\/01621459.2016.1192039","article-title":"The generalized higher criticism for testing SNP-set effects in genetic association studies","volume":"112","author":"Barnett,","year":"2017","journal-title":"J. Am. Statist. Assoc."},{"key":"2023021111212296000_B2","doi-asserted-by":"crossref","first-page":"791","DOI":"10.1093\/biomet\/asr043","article-title":"Square-root lasso: pivotal recovery of sparse signals via conic programming","volume":"98","author":"Belloni,","year":"2011","journal-title":"Biometrika"},{"key":"2023021111212296000_B3","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. Statist."},{"key":"2023021111212296000_B4","doi-asserted-by":"crossref","first-page":"1111","DOI":"10.1214\/13-AOS1096","article-title":"A lasso for hierarchical interactions","volume":"41","author":"Bien,","year":"2013","journal-title":"Ann. 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