{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,5]],"date-time":"2024-09-05T12:42:37Z","timestamp":1725540157283},"reference-count":14,"publisher":"Oxford University Press (OUP)","issue":"1","license":[{"start":{"date-parts":[[2021,2,16]],"date-time":"2021-02-16T00:00:00Z","timestamp":1613433600000},"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":[[2022,2,1]]},"abstract":"<jats:title>Summary<\/jats:title>\n               <jats:p>Post-selection inference on thousands of parameters has attracted considerable research interest in recent years. Specifically, Benjamini &amp; Yekutieli (2005) considered constructing confidence intervals after selection. They proposed adjusting the confidence levels of marginal confidence intervals for the selected parameters to ensure control of the false coverage-statement rate. However, although Benjamini\u2013Yekutieli confidence intervals are widely used, they are uniformly inflated. In this article, two methods for narrowing the Benjamini\u2013Yekutieli confidence intervals are proposed. The first improves the confidence intervals by incorporating the selection event into the calculation. The second method further narrows those confidence intervals in which some parameters are selected with very small probabilities, which results in underutilization of the target level for control of the false coverage-statement rate. A breast cancer dataset is analysed to compare the methods.<\/jats:p>","DOI":"10.1093\/biomet\/asab010","type":"journal-article","created":{"date-parts":[[2021,2,15]],"date-time":"2021-02-15T20:24:33Z","timestamp":1613420673000},"page":"153-164","source":"Crossref","is-referenced-by-count":1,"title":["General ways to improve false coverage rate-adjusted selective confidence intervals"],"prefix":"10.1093","volume":"109","author":[{"given":"Haibing","family":"Zhao","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2021,2,16]]},"reference":[{"key":"2022020204422907900_B1","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1198\/016214504000001907","article-title":"False discovery rate-adjusted multiple confidence intervals for selected parameters","volume":"100","author":"Benjamini,","year":"2005","journal-title":"J. Am. Statist. 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Assoc."},{"key":"2022020204422907900_B9","author":"Weinstein,","year":"2019","journal-title":"Online control of the false coverage rate and false sign rate"},{"key":"2022020204422907900_B10","first-page":"531","article-title":"Selective sign-determining multiple confidence intervals with FCR control","volume":"30","author":"Weinstein,","year":"2020","journal-title":"Statist. Sinica"},{"key":"2022020204422907900_B11","doi-asserted-by":"crossref","first-page":"1098","DOI":"10.1111\/biom.13222","article-title":"Constructing confidence intervals for selected parameters","volume":"76","author":"Zhao,","year":"2020","journal-title":"Biometrics"},{"key":"2022020204422907900_B12","doi-asserted-by":"crossref","first-page":"871","DOI":"10.1111\/j.1467-9868.2012.01033.x","article-title":"Empirical Bayes false coverage rate controlling confidence intervals","volume":"B 74","author":"Zhao,","year":"2012","journal-title":"J. R. Statist. Soc."},{"key":"2022020204422907900_B13","first-page":"725","article-title":"A Bayesian approach to construct multiple confidence intervals of selected parameters with sparse signals","volume":"25","author":"Zhao,","year":"2015","journal-title":"Statist. Sinica"},{"key":"2022020204422907900_B14","doi-asserted-by":"crossref","first-page":"621","DOI":"10.1093\/biostatistics\/kxn001","article-title":"Bias-reduced estimators and confidence intervals for odds ratios in genome-wide association studies","volume":"9","author":"Zhong,","year":"2008","journal-title":"Biostatistics"}],"container-title":["Biometrika"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/academic.oup.com\/biomet\/advance-article-pdf\/doi\/10.1093\/biomet\/asab010\/36276216\/asab010.pdf","content-type":"application\/pdf","content-version":"am","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/biomet\/article-pdf\/109\/1\/153\/42362024\/asab010.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/biomet\/article-pdf\/109\/1\/153\/42362024\/asab010.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,2,2]],"date-time":"2022-02-02T04:42:47Z","timestamp":1643776967000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/biomet\/article\/109\/1\/153\/6137832"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,2,16]]},"references-count":14,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2021,2,16]]},"published-print":{"date-parts":[[2022,2,1]]}},"URL":"https:\/\/doi.org\/10.1093\/biomet\/asab010","relation":{},"ISSN":["0006-3444","1464-3510"],"issn-type":[{"value":"0006-3444","type":"print"},{"value":"1464-3510","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2022,3,1]]},"published":{"date-parts":[[2021,2,16]]}}}