{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,24]],"date-time":"2026-09-24T12:40:49Z","timestamp":1790253649943,"version":"4.1.0"},"reference-count":37,"publisher":"Oxford University Press (OUP)","issue":"2","license":[{"start":{"date-parts":[[2023,3,13]],"date-time":"2023-03-13T00:00:00Z","timestamp":1678665600000},"content-version":"vor","delay-in-days":4148,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"funder":[{"DOI":"10.13039\/100000001","name":"US National Science Foundation","doi-asserted-by":"publisher","award":["NSF-0934617"],"award-info":[{"award-number":["NSF-0934617"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2012,3,1]]},"abstract":"<jats:title>Summary<\/jats:title><jats:p>For a reduced rank multivariate stochastic regression model of rank r*, the regression coefficient matrix can be expressed as a sum of r* unit rank matrices each of which is proportional to the outer product of the left and right singular vectors. For improving predictive accuracy and facilitating interpretation, it is often desirable that these left and right singular vectors be sparse or enjoy some smoothness property. We propose a regularized reduced rank regression approach for solving this problem. Computation algorithms and regularization parameter selection methods are developed, and the properties of the new method are explored both theoretically and by simulation. In particular, the regularization method proposed is shown to be selection consistent and asymptotically normal and to enjoy the oracle property. We apply the proposed model to perform biclustering analysis with microarray gene expression data.<\/jats:p>","DOI":"10.1111\/j.1467-9868.2011.01002.x","type":"journal-article","created":{"date-parts":[[2011,11,3]],"date-time":"2011-11-03T17:54:21Z","timestamp":1320342861000},"page":"203-221","source":"Crossref","is-referenced-by-count":99,"title":["Reduced Rank Stochastic Regression with a Sparse Singular value Decomposition"],"prefix":"10.1093","volume":"74","author":[{"given":"Kun","family":"Chen","sequence":"first","affiliation":[{"name":"Kansas State University , Manhattan , USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Kung-Sik","family":"Chan","sequence":"additional","affiliation":[{"name":"University of Iowa , Iowa City , USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Nils Chr.","family":"Stenseth","sequence":"additional","affiliation":[{"name":"University of Oslo , Norway"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2011,11,3]]},"reference":[{"key":"2023031400060062600_","doi-asserted-by":"crossref","first-page":"327","DOI":"10.1214\/aoms\/1177729580","article-title":"Estimating linear restrictions on regression coefficients for multivariate normal distributions","volume":"22","author":"Anderson","year":"1951","journal-title":"Ann. Math. Statist."},{"key":"2023031400060062600_","first-page":"193","article-title":"Specification and misspecification in reduced rank regression","volume":"64","author":"Anderson","year":"2002","journal-title":"Sankhya"},{"key":"2023031400060062600_","volume-title":"An Introduction to Multivariate Statistical Analysis","author":"Anderson","year":"2003"},{"key":"2023031400060062600_","doi-asserted-by":"crossref","first-page":"13790","DOI":"10.1073\/pnas.191502998","article-title":"Classification of human lung carcinomas by mrna expression profiling reveals distinct adenocarcinoma subclasses","volume":"98","author":"Bhattacharjee","year":"2001","journal-title":"Proc. Natn. Acad. Sci. USA"},{"key":"2023031400060062600_","doi-asserted-by":"crossref","first-page":"369","DOI":"10.4310\/SII.2009.v2.n3.a10","article-title":"Penalized methods for bi-level variable selection","volume":"2","author":"Breheny","year":"2009","journal-title":"Statist. Interface"},{"key":"2023031400060062600_","doi-asserted-by":"crossref","first-page":"1282","DOI":"10.1214\/11-AOS876","article-title":"Optimal selection of reduced rank estimators of high-dimensional matrices","volume":"39","author":"Bunea","year":"2011","journal-title":"Ann. Statist."},{"key":"2023031400060062600_","doi-asserted-by":"crossref","first-page":"2964","DOI":"10.1016\/j.cor.2007.01.005","article-title":"Biclustering in data mining","volume":"35","author":"Busygin","year":"2008","journal-title":"Comput. Oper. Res."},{"key":"2023031400060062600_","doi-asserted-by":"crossref","first-page":"145","DOI":"10.1198\/073500102288618847","article-title":"Tests of rank in reduced rank regression models","volume":"21","author":"Camba-Mendez","year":"2003","journal-title":"J. Bus. Econ. Statist."},{"key":"2023031400060062600_","doi-asserted-by":"crossref","first-page":"1200","DOI":"10.1080\/01621459.1995.10476626","article-title":"Adapting to unknown smoothness via wavelet shrinkage","volume":"90","author":"Donoho","year":"1995","journal-title":"J. Am. Statist. Ass."},{"key":"2023031400060062600_","doi-asserted-by":"crossref","first-page":"407","DOI":"10.1214\/009053604000000067","article-title":"Least angle regression","volume":"32","author":"Efron","year":"2004","journal-title":"Ann. Statist."},{"key":"2023031400060062600_","doi-asserted-by":"crossref","first-page":"1348","DOI":"10.1198\/016214501753382273","article-title":"Variable selection via nonconcave penalized likelihood and its oracle properties","volume":"96","author":"Fan","year":"2001","journal-title":"J. Am. Statist. Ass."},{"key":"2023031400060062600_","first-page":"302","article-title":"Pathwise coordinate optimization","volume":"2","author":"Friedman","year":"2007","journal-title":"Ann. Appl. Statist."},{"key":"2023031400060062600_","first-page":"1","article-title":"Regularization paths for generalized linear models via coordinate descent","volume":"33","author":"Friedman","year":"2010","journal-title":"J. Statist. Softwr."},{"key":"2023031400060062600_","doi-asserted-by":"crossref","first-page":"373","DOI":"10.1007\/s00186-007-0161-1","article-title":"Biconvex sets and optimization with biconvex functions: a survey and extensions","volume":"66","author":"Gorski","year":"2007","journal-title":"Math. Meth. Oper. Res."},{"key":"2023031400060062600_","doi-asserted-by":"crossref","first-page":"248","DOI":"10.1016\/0047-259X(75)90042-1","article-title":"Reduced-rank regression for the multivariate linear model","volume":"5","author":"Izenman","year":"1975","journal-title":"J. Multiv. Anal."},{"key":"2023031400060062600_","doi-asserted-by":"crossref","first-page":"1087","DOI":"10.1111\/j.1541-0420.2010.01392.x","article-title":"Biclustering via sparse singular value decomposition","volume":"66","author":"Lee","year":"2010","journal-title":"Biometrics"},{"key":"2023031400060062600_","doi-asserted-by":"crossref","first-page":"e161","DOI":"10.1371\/journal.pgen.0030161","article-title":"Capturing heterogeneity in gene expression studies by surrogate variable analysis","volume":"3","author":"Leek","year":"2007","journal-title":"PLOS Genet."},{"key":"2023031400060062600_","doi-asserted-by":"crossref","first-page":"1281","DOI":"10.1198\/016214508000000454","article-title":"Statistical significance of clustering for high-dimension, low sample size data","volume":"103","author":"Liu","year":"2008","journal-title":"J. Am. Statist. Ass."},{"key":"2023031400060062600_","volume-title":"Technical Report","author":"Obozinski","year":"2008"},{"key":"2023031400060062600_","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1214\/09-AOAS271","article-title":"Regularized multivariate regression for identifying master predictors with application to integrative genomics study of breast cancer","volume":"4","author":"Peng","year":"2010","journal-title":"Ann. Appl. Statist."},{"key":"2023031400060062600_","volume-title":"R: a Language and Environment for Statistical Computing","author":"R Development Core Team","year":"2008"},{"key":"2023031400060062600_","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4757-2853-8","volume-title":"Multivariate Reduced-rank Regression: Theory and Applications","author":"Reinsel","year":"1998"},{"key":"2023031400060062600_","volume-title":"Matrix Analysis for Statistics","author":"Schott","year":"2005"},{"key":"2023031400060062600_","first-page":"1085","article-title":"Ecological and genetic impact of Atlantic cod larval drift in the Skagerrak","volume":"273","author":"Stenseth","year":"2006","journal-title":"Proc. R. Soc. Lond."},{"key":"2023031400060062600_","doi-asserted-by":"crossref","first-page":"509","DOI":"10.1093\/biomet\/61.3.509","article-title":"Cross-validation and multinomial prediction","volume":"61","author":"Stone","year":"1974","journal-title":"Biometrika"},{"key":"2023031400060062600_","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","year":"1996","journal-title":"J. R. Statist. Soc."},{"key":"2023031400060062600_","first-page":"615","article-title":"An accelerated proximal gradient algorithm for nuclear norm regularized least squares problems","volume":"6","author":"Toh","year":"2009","journal-title":"Pacif. J. Optim."},{"key":"2023031400060062600_","doi-asserted-by":"crossref","first-page":"349","DOI":"10.1198\/004017005000000139","article-title":"Simultaneous variable selection","volume":"47","author":"Turlach","year":"2005","journal-title":"Technometrics"},{"key":"2023031400060062600_","volume-title":"Asymptotic Statistics","author":"van der Vaart","year":"2000"},{"key":"2023031400060062600_","doi-asserted-by":"crossref","first-page":"1147","DOI":"10.1016\/j.neuroimage.2010.07.002","article-title":"Discovering genetic associations with high-dimensional neuroimaging phenotypes: a sparse reduced-rank regression approach","volume":"53","author":"Vounou","year":"2010","journal-title":"NeuroImage"},{"key":"2023031400060062600_","doi-asserted-by":"crossref","first-page":"515","DOI":"10.1093\/biostatistics\/kxp008","article-title":"A penalized matrix decomposition, with applications to sparse principal components and canonical correlation analysis","volume":"10","author":"Witten","year":"2009","journal-title":"Biostatistics"},{"key":"2023031400060062600_","doi-asserted-by":"crossref","first-page":"329","DOI":"10.1111\/j.1467-9868.2007.00591.x","article-title":"Dimension reduction and coefficient estimation in multivariate linear regression","volume":"69","author":"Yuan","year":"2007","journal-title":"J. R. Statist. Soc."},{"key":"2023031400060062600_","doi-asserted-by":"crossref","first-page":"1567","DOI":"10.1214\/07-AOS520","article-title":"The sparsity and bias of the lasso selection in high-dimensional linear regression","volume":"36","author":"Zhang","year":"2008","journal-title":"Ann. Statist."},{"key":"2023031400060062600_","first-page":"2541","article-title":"On model selection consistency of lasso","volume":"7","author":"Zhao","year":"2006","journal-title":"J. Mach. Learn. Res."},{"key":"2023031400060062600_","doi-asserted-by":"crossref","first-page":"1418","DOI":"10.1198\/016214506000000735","article-title":"The adaptive lasso and its oracle properties","volume":"101","author":"Zou","year":"2006","journal-title":"J. Am. Statist. Ass."},{"key":"2023031400060062600_","doi-asserted-by":"crossref","first-page":"301","DOI":"10.1111\/j.1467-9868.2005.00503.x","article-title":"Regularization and variable selection via the elastic net","volume":"67","author":"Zou","year":"2005","journal-title":"J. R. Statist. Soc."},{"key":"2023031400060062600_","doi-asserted-by":"crossref","first-page":"2173","DOI":"10.1214\/009053607000000127","article-title":"On the degree of freedom of the lasso","volume":"35","author":"Zou","year":"2007","journal-title":"Ann. Statist."}],"container-title":["Journal of the Royal Statistical Society Series B: Statistical Methodology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1111%2Fj.1467-9868.2011.01002.x","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/academic.oup.com\/jrsssb\/article-pdf\/74\/2\/203\/49513791\/jrsssb_74_2_203.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/jrsssb\/article-pdf\/74\/2\/203\/49513791\/jrsssb_74_2_203.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,3,13]],"date-time":"2025-03-13T19:31:24Z","timestamp":1741894284000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/jrsssb\/article\/74\/2\/203\/7075303"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,11,3]]},"references-count":37,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2011,11,3]]},"published-print":{"date-parts":[[2012,3,1]]}},"URL":"https:\/\/doi.org\/10.1111\/j.1467-9868.2011.01002.x","relation":{},"ISSN":["1369-7412","1467-9868"],"issn-type":[{"value":"1369-7412","type":"print"},{"value":"1467-9868","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2012,3]]},"published":{"date-parts":[[2011,11,3]]}}}