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A major task in analyzing these gene expression data is to identify both over\u2010expressed and under\u2010expressed genes. The popular two\u2010group models select the non\u2010null genes without further classifying them as overexpression or underexpression. Consequently, two\u2010group decision rules are unable to constrain the numbers of falsely discovered over\u2010expressed or under\u2010expressed genes respectively. We propose a general three\u2010group model that allows dependence between the test statistics and develop a decision rule that separately controls the two types of false discoveries. We show that the optimal decision rule in our three\u2010group model has a special monotonic structure. By making use of this monotonic structure, we can linearize the two\u2010directional false discovery rate constraints. We prove that our decision rule optimizes the expected number of true discoveries while controlling the proportions of falsely discovered over\u2010expressed and under\u2010expressed genes at desired levels simultaneously. The data\u2010driven versions of the proposed procedures are suggested, and their consistency is established. Comparisons with state\u2010of\u2010the\u2010art approaches and applications to genomic studies show that our procedures work well.<\/jats:p>","DOI":"10.1002\/sim.10329","type":"journal-article","created":{"date-parts":[[2025,2,6]],"date-time":"2025-02-06T05:21:01Z","timestamp":1738819261000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Optimal Control of Directional False Discovery Rates in Large\u2010Scale Testing"],"prefix":"10.1002","volume":"44","author":[{"given":"Guozhu","family":"Tang","sequence":"first","affiliation":[{"name":"KLATASDS\u2010MOE, School of Statistics East China Normal University  Shanghai China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yicheng","family":"Kang","sequence":"additional","affiliation":[{"name":"Department of Information Systems &amp; Analytics Miami University  Ohio 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