{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,15]],"date-time":"2026-10-15T06:14:34Z","timestamp":1792044874767,"version":"4.4.0"},"reference-count":147,"publisher":"Oxford University Press (OUP)","issue":"4","license":[{"start":{"date-parts":[[2013,8,12]],"date-time":"2013-08-12T00:00:00Z","timestamp":1376265600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"funder":[{"DOI":"10.13039\/100000002","name":"National Institutes of Health","doi-asserted-by":"publisher","award":["R01GM100474-01"],"award-info":[{"award-number":["R01GM100474-01"]}],"id":[{"id":"10.13039\/100000002","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000002","name":"National Institutes of Health","doi-asserted-by":"publisher","award":["R01-GM072611"],"award-info":[{"award-number":["R01-GM072611"]}],"id":[{"id":"10.13039\/100000002","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000002","name":"National Institutes of Health","doi-asserted-by":"publisher","award":["DMS-0704337"],"award-info":[{"award-number":["DMS-0704337"]}],"id":[{"id":"10.13039\/100000002","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Bendheim Center for Finance at Princeton University"},{"DOI":"10.13039\/100006734","name":"Princeton University","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100006734","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2013,9,1]]},"abstract":"<jats:title>Summary<\/jats:title>\n                  <jats:p>The paper deals with the estimation of a high dimensional covariance with a conditional sparsity structure and fast diverging eigenvalues. By assuming a sparse error covariance matrix in an approximate factor model, we allow for the presence of some cross-sectional correlation even after taking out common but unobservable factors. We introduce the principal orthogonal complement thresholding method \u2018POET\u2019 to explore such an approximate factor structure with sparsity. The POET-estimator includes the sample covariance matrix, the factor-based covariance matrix, the thresholding estimator and the adaptive thresholding estimator as specific examples. We provide mathematical insights when the factor analysis is approximately the same as the principal component analysis for high dimensional data. The rates of convergence of the sparse residual covariance matrix and the conditional sparse covariance matrix are studied under various norms. It is shown that the effect of estimating the unknown factors vanishes as the dimensionality increases. The uniform rates of convergence for the unobserved factors and their factor loadings are derived. The asymptotic results are also verified by extensive simulation studies. Finally, a real data application on portfolio allocation is presented.<\/jats:p>","DOI":"10.1111\/rssb.12016","type":"journal-article","created":{"date-parts":[[2013,8,12]],"date-time":"2013-08-12T07:19:59Z","timestamp":1376291999000},"page":"603-680","source":"Crossref","is-referenced-by-count":757,"title":["Large Covariance Estimation by Thresholding Principal Orthogonal Complements"],"prefix":"10.1093","volume":"75","author":[{"given":"Jianqing","family":"Fan","sequence":"first","affiliation":[{"name":"Princeton University , USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yuan","family":"Liao","sequence":"additional","affiliation":[{"name":"University of Maryland , College Park , USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Martina","family":"Mincheva","sequence":"additional","affiliation":[{"name":"Princeton University , USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2013,8,12]]},"reference":[{"key":"2023031109460667900_","doi-asserted-by":"crossref","first-page":"1171","DOI":"10.1214\/12-AOS1000","article-title":"Noisy matrix decomposition via convex relaxation: optimal rates in high dimensions","volume":"40","author":"Agarwal","year":"2012","journal-title":"Ann. Statist."},{"key":"2023031109460667900_","doi-asserted-by":"crossref","first-page":"219","DOI":"10.1016\/S0304-4076(00)00083-X","article-title":"GMM estimation of linear panel data models with time-varying individual effects","volume":"101","author":"Ahn","year":"2001","journal-title":"J. Econmetr."},{"key":"2023031109460667900_","doi-asserted-by":"crossref","first-page":"1806","DOI":"10.1016\/j.spl.2010.08.005","article-title":"Improved penalization for determining the number of factors in approximate factor models","volume":"80","author":"Alessi","year":"2010","journal-title":"Statist. Probab. Lett."},{"key":"2023031109460667900_","doi-asserted-by":"crossref","first-page":"2877","DOI":"10.1214\/08-AOS664","article-title":"High-dimensional analysis of semidefinite relaxations for sparse principal components","volume":"37","author":"Amini","year":"2009","journal-title":"Ann. Statist."},{"key":"2023031109460667900_","doi-asserted-by":"crossref","first-page":"939","DOI":"10.1198\/016214501753208942","article-title":"Regularized wavelet approximations","volume":"96","author":"Antoniadis","year":"2001","journal-title":"J. Am. Statist. Ass."},{"key":"2023031109460667900_","first-page":"1269","article-title":"Optimal solutions for sparse principal component analysis","volume":"9","author":"d\u2019Aspremont","year":"2008","journal-title":"J. Mach. Learn. Res."},{"key":"2023031109460667900_","volume-title":"Measure Theory and Probability Theory","author":"Athreya","year":"2006"},{"key":"2023031109460667900_","doi-asserted-by":"crossref","first-page":"135","DOI":"10.1111\/1468-0262.00392","article-title":"Inferential theory for factor models of large dimensions","volume":"71","author":"Bai","year":"2003","journal-title":"Econometrica"},{"key":"2023031109460667900_","doi-asserted-by":"crossref","first-page":"191","DOI":"10.1111\/1468-0262.00273","article-title":"Determining the number of factors in approximate factor models","volume":"70","author":"Bai","year":"2002","journal-title":"Econometrica"},{"key":"2023031109460667900_","doi-asserted-by":"crossref","first-page":"89","DOI":"10.1561\/0800000002","article-title":"Large dimensional factor analysis","volume":"3","author":"Bai","year":"2008","journal-title":"Found. Trends Econmetr."},{"key":"2023031109460667900_","first-page":"199","article-title":"Estimating high dimensional covariance matrices and its applications","volume":"12","author":"Bai","year":"2011","journal-title":"Ann. Econ. Finan."},{"key":"2023031109460667900_","doi-asserted-by":"crossref","first-page":"2577","DOI":"10.1214\/08-AOS600","article-title":"Covariance regularization by thresholding","volume":"36","author":"Bickel","year":"2008","journal-title":"Ann. Statist."},{"key":"2023031109460667900_","article-title":"Minimax bounds for sparse PCA with noisy high-dimensional data","author":"Birnbaum","year":"2012","journal-title":"Ann. Statist."},{"key":"2023031109460667900_","doi-asserted-by":"crossref","first-page":"169","DOI":"10.1016\/j.jeconom.2005.01.027","article-title":"Are more data always better for factor analysis?","volume":"132","author":"Boivin","year":"2006","journal-title":"J. Econmetr."},{"key":"2023031109460667900_","doi-asserted-by":"crossref","first-page":"1956","DOI":"10.1137\/080738970","article-title":"A singular value thresholding algorithm for matrix completion","volume":"20","author":"Cai","year":"2008","journal-title":"SIAM J. Optimizn"},{"key":"2023031109460667900_","doi-asserted-by":"crossref","first-page":"672","DOI":"10.1198\/jasa.2011.tm10560","article-title":"Adaptive thresholding for sparse covariance matrix estimation","volume":"106","author":"Cai","year":"2011","journal-title":"J. Am. Statist. Ass."},{"key":"2023031109460667900_","first-page":"2389","volume-title":"Ann. Statist.","author":"Cai","year":"2012"},{"key":"2023031109460667900_","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1145\/1970392.1970395","article-title":"Robust principal component analysis?","volume":"58","author":"Cand\u00e8s","year":"2011","journal-title":"J. Ass. Comput. Mach."},{"key":"2023031109460667900_","doi-asserted-by":"crossref","first-page":"1438","DOI":"10.1198\/016214508000000869","article-title":"High-dimensional sparse factor modeling: applications in gene expression genomics","volume":"103","author":"Carvalho","year":"2008","journal-title":"J. Am. Statist. Ass."},{"key":"2023031109460667900_","doi-asserted-by":"crossref","first-page":"1305","DOI":"10.2307\/1912276","article-title":"Arbitrage, factor structure and mean-variance analysis in large asset markets","volume":"51","author":"Chamberlain","year":"1983","journal-title":"Econometrica"},{"key":"2023031109460667900_","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1137\/0707001","article-title":"The rotation of eigenvectors by a perturbation III","volume":"7","author":"Davis","year":"1970","journal-title":"SIAM J. Numer. Anal."},{"key":"2023031109460667900_","doi-asserted-by":"crossref","first-page":"188","DOI":"10.1016\/j.jeconom.2011.02.012","article-title":"A two-step estimator for large approximate dynamic factor models based on Kalman filtering","volume":"164","author":"Doz","year":"2011","journal-title":"J. Econmetr."},{"key":"2023031109460667900_","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1198\/016214506000001211","article-title":"Correlation and large-scale simultaneous significance testing","volume":"102","author":"Efron","year":"2007","journal-title":"J. Am. Statist. Ass."},{"key":"2023031109460667900_","doi-asserted-by":"crossref","first-page":"1042","DOI":"10.1198\/jasa.2010.tm09129","article-title":"Correlated z-values and the accuracy of large-scale statistical estimates","volume":"105","author":"Efron","year":"2010","journal-title":"J. Am. Statist. Ass."},{"key":"2023031109460667900_","doi-asserted-by":"crossref","first-page":"427","DOI":"10.1111\/j.1540-6261.1992.tb04398.x","article-title":"The cross-section of expected stock returns","volume":"47","author":"Fama","year":"1992","journal-title":"J. Finan."},{"key":"2023031109460667900_","doi-asserted-by":"crossref","first-page":"186","DOI":"10.1016\/j.jeconom.2008.09.017","article-title":"High dimensional covariance matrix estimation using a factor model","volume":"147","author":"Fan","year":"2008","journal-title":"J. Econmetr."},{"key":"2023031109460667900_","doi-asserted-by":"crossref","first-page":"1019","DOI":"10.1080\/01621459.2012.720478","article-title":"Control of the false discovery rate under arbitrary covariance dependence (with discussion)","volume":"107","author":"Fan","year":"2012","journal-title":"J. Am. Statist. Ass."},{"key":"2023031109460667900_","doi-asserted-by":"crossref","first-page":"3320","DOI":"10.1214\/11-AOS944","article-title":"High dimensional covariance matrix estimation in approximate factor models","volume":"39","author":"Fan","year":"2011","journal-title":"Ann. Statist."},{"key":"2023031109460667900_","doi-asserted-by":"crossref","DOI":"10.2139\/ssrn.1977673","volume-title":"Large covariance estimation by thresholding principal orthogonal complements","author":"Fan","year":"2011"},{"key":"2023031109460667900_","doi-asserted-by":"crossref","first-page":"592","DOI":"10.1080\/01621459.2012.682825","article-title":"Vast portfolio selection with gross-exposure constraints","volume":"107","author":"Fan","year":"2012","journal-title":"J. Am. Statist. Ass."},{"key":"2023031109460667900_","doi-asserted-by":"crossref","first-page":"540","DOI":"10.1162\/003465300559037","article-title":"The generalized dynamic factor model: identification and estimation","volume":"82","author":"Forni","year":"2000","journal-title":"Rev. Econ. Statist."},{"key":"2023031109460667900_","doi-asserted-by":"crossref","first-page":"231","DOI":"10.1016\/S0304-4076(03)00196-9","article-title":"The generalized dynamic factor model consistency and rates","volume":"119","author":"Forni","year":"2004","journal-title":"J. Econmetr."},{"key":"2023031109460667900_","doi-asserted-by":"crossref","first-page":"1113","DOI":"10.1017\/S0266466601176048","article-title":"The generalized dynamic factor model: representation theory","volume":"17","author":"Forni","year":"2001","journal-title":"Econmetr. Theor."},{"key":"2023031109460667900_","volume-title":"Manuscript","author":"Fryzlewicz","year":"2012"},{"key":"2023031109460667900_","doi-asserted-by":"crossref","first-page":"603","DOI":"10.1198\/016214506000001275","article-title":"Determining the number of factors in the general dynamic factor model","volume":"102","author":"Hallin","year":"2007","journal-title":"J. Am. Statist. Ass."},{"key":"2023031109460667900_","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1016\/j.jeconom.2010.11.004","article-title":"Dynamic factors in the presence of blocks","volume":"163","author":"Hallin","year":"2011","journal-title":"J. Econmetr."},{"key":"2023031109460667900_","doi-asserted-by":"crossref","DOI":"10.1007\/978-0-387-84858-7","volume-title":"The Elements of Statistical Learning: Data Mining, Inference, and Prediction","author":"Hastie","year":"2009"},{"key":"2023031109460667900_","first-page":"361","volume-title":"Proc. 4th Berkeley Symp. Mathematical Statistics and Probability","author":"James","year":"1961"},{"key":"2023031109460667900_","doi-asserted-by":"crossref","first-page":"295","DOI":"10.1214\/aos\/1009210544","article-title":"On the distribution of the largest eigenvalue in principal components analysis","volume":"29","author":"Johnstone","year":"2001","journal-title":"Ann. Statist."},{"key":"2023031109460667900_","doi-asserted-by":"crossref","first-page":"682","DOI":"10.1198\/jasa.2009.0121","article-title":"On consistency and sparsity for principal components analysis in high dimensions","volume":"104","author":"Johnstone","year":"2009","journal-title":"J. Am. Statist. Ass."},{"key":"2023031109460667900_","doi-asserted-by":"crossref","first-page":"4104","DOI":"10.1214\/09-AOS709","article-title":"PCA consistency in high dimension, low sample size context","volume":"37","author":"Jung","year":"2009","journal-title":"Ann. Statist."},{"key":"2023031109460667900_","doi-asserted-by":"crossref","first-page":"397","DOI":"10.1198\/jbes.2009.07239","article-title":"A testing procedure for determining the number of factors in approximate factor models with large datasets","volume":"28","author":"Kapetanios","year":"2010","journal-title":"J. Bus. Econ. Statist."},{"key":"2023031109460667900_","doi-asserted-by":"crossref","first-page":"4254","DOI":"10.1214\/09-AOS720","article-title":"Sparsistency and rates of convergence in large covariance matrix estimation","volume":"37","author":"Lam","year":"2009","journal-title":"Ann. Statist."},{"key":"2023031109460667900_","volume-title":"Factor Analysis as a Statistical Method","author":"Lawley","year":"1971"},{"key":"2023031109460667900_","doi-asserted-by":"crossref","first-page":"18718","DOI":"10.1073\/pnas.0808709105","article-title":"A general framework for multiple testing dependence","volume":"105","author":"Leek","year":"2008","journal-title":"Proc. Natn. Acad. Sci. USA"},{"key":"2023031109460667900_","volume-title":"Int. Wrkshp Computational Advances in Multi-Sensor Adaptive Processing, Aruba","author":"Lin","year":"2009"},{"key":"2023031109460667900_","volume-title":"Manuscript","author":"Luo","year":"2011"},{"key":"2023031109460667900_","volume-title":"Ann. Statist","author":"Ma","year":"2013"},{"key":"2023031109460667900_","doi-asserted-by":"crossref","first-page":"1436","DOI":"10.1214\/009053606000000281","article-title":"High dimensional graphs and variable selection with the Lasso","volume":"34","author":"Meinshausen","year":"2006","journal-title":"Ann. Statist."},{"key":"2023031109460667900_","doi-asserted-by":"crossref","first-page":"1004","DOI":"10.1162\/REST_a_00043","article-title":"Determining the number of factors from empirical distribution of eigenvalues","volume":"92","author":"Onatski","year":"2010","journal-title":"Rev. Econ. Statist."},{"key":"2023031109460667900_","volume-title":"Manuscript","author":"Pati","year":"2012"},{"key":"2023031109460667900_","first-page":"1617","article-title":"Asymptotics of sample eigenstructure for a large dimensional spiked covariance model","volume":"17","author":"Paul","year":"2007","journal-title":"Statist. Sin."},{"key":"2023031109460667900_","doi-asserted-by":"crossref","first-page":"967","DOI":"10.1111\/j.1468-0262.2006.00692.x","article-title":"Estimation and inference in large heterogeneous panels with a multifactor error structure","volume":"74","author":"Pesaran","year":"2006","journal-title":"Econometrica"},{"key":"2023031109460667900_","article-title":"Testing CAPM with a large number of assets","author":"Pesaran","year":"2012","journal-title":"American Finance Association San Diego Meetings Paper"},{"key":"2023031109460667900_","volume-title":"Manuscript","author":"Phan","year":"2012"},{"key":"2023031109460667900_","doi-asserted-by":"crossref","first-page":"341","DOI":"10.1016\/0022-0531(76)90046-6","article-title":"The arbitrage theory of capital asset pricing","volume":"13","author":"Ross","year":"1976","journal-title":"J. Econ. Theor."},{"key":"2023031109460667900_","doi-asserted-by":"crossref","first-page":"177","DOI":"10.1198\/jasa.2009.0101","article-title":"Generalized thresholding of large covariance matrices","volume":"104","author":"Rothman","year":"2009","journal-title":"J. Am. Statist. Ass."},{"key":"2023031109460667900_","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1111\/j.1368-423X.2009.00295.x","article-title":"The econometrics of mean-variance efficiency tests: a survey","volume":"12","author":"Sentana","year":"2009","journal-title":"Econometr. J."},{"key":"2023031109460667900_","first-page":"425","article-title":"Capital asset prices: a theory of market equilibrium under conditions of risks","volume":"19","author":"Sharpe","year":"1964","journal-title":"J. Finan."},{"key":"2023031109460667900_","doi-asserted-by":"crossref","first-page":"1015","DOI":"10.1016\/j.jmva.2007.06.007","article-title":"Sparse principal component analysis via regularized low rank matrix approximation","volume":"99","author":"Shen","year":"2008","journal-title":"J. Multiv. Anal."},{"key":"2023031109460667900_","doi-asserted-by":"crossref","DOI":"10.3386\/w6702","volume-title":"Diffusion Indexes","author":"Stock","year":"1998"},{"key":"2023031109460667900_","doi-asserted-by":"crossref","first-page":"1167","DOI":"10.1198\/016214502388618960","article-title":"Forecasting using principal components from a large number of predictors","volume":"97","author":"Stock","year":"2002","journal-title":"J. Am. Statist. Ass."},{"key":"2023031109460667900_","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":"2023031109460667900_","volume-title":"New. Inform. Process. Syst","author":"Wright","year":"2009"},{"key":"2023031109460667900_","doi-asserted-by":"crossref","first-page":"305","DOI":"10.1534\/genetics.111.129221","article-title":"A flexible estimating equations approach for mapping function-valued traits","volume":"189","author":"Xiong","year":"2011","journal-title":"Genetics"},{"key":"2023031109460667900_","doi-asserted-by":"crossref","first-page":"1068","DOI":"10.1111\/j.1541-0420.2009.01222.x","article-title":"Nonparametric modeling of longitudinal covariance structure in functional mapping of quantitative trait loci","volume":"65","author":"Yap","year":"2009","journal-title":"Biometrics"},{"key":"2023031109460667900_","article-title":"Large-scale sparse principal component analysis with application to text data","author":"Zhang","year":"2011","journal-title":"New. Inform. Process. Syst"},{"key":"2023031109460667900_","volume-title":"Model-free estimation of large variance matrices","author":"Abadir","year":"2010"},{"key":"2023031109460667900_","doi-asserted-by":"crossref","first-page":"1171","DOI":"10.1214\/12-AOS1000","article-title":"Noisy matrix decomposition via convex relaxation: optimal rates in high dimensions","volume":"40","author":"Agarwal","year":"2012","journal-title":"Ann. Statist."},{"key":"2023031109460667900_","doi-asserted-by":"crossref","first-page":"6745","DOI":"10.1073\/pnas.96.12.6745","article-title":"Broad patterns of gene expression revealed by clustering analysis of tumor and normal colon tissues probed by oligonucleotide arrays","volume":"96","author":"Alon","year":"1999","journal-title":"Proc. Natn. Acad. Sci. USA"},{"key":"2023031109460667900_","doi-asserted-by":"crossref","first-page":"2877","DOI":"10.1214\/08-AOS664","article-title":"High-dimensional analysis of semidefinite relaxations for sparse principal components","volume":"37","author":"Amini","year":"2009","journal-title":"Ann. Statist."},{"key":"2023031109460667900_","doi-asserted-by":"crossref","first-page":"16","DOI":"10.1214\/07-SS014","article-title":"Wavelet methods in statistics: some recent developments and their application","volume":"1","author":"Antoniadis","year":"2007","journal-title":"Statist. Surv."},{"key":"2023031109460667900_","doi-asserted-by":"crossref","first-page":"436","DOI":"10.1214\/11-AOS966","article-title":"Statistical analysis of factor models of high dimension","volume":"40","author":"Bai","year":"2012","journal-title":"Ann. Statist."},{"key":"2023031109460667900_","doi-asserted-by":"crossref","first-page":"191","DOI":"10.1111\/1468-0262.00273","article-title":"Determining the number of factors in approximate factor models","volume":"70","author":"Bai","year":"2002","journal-title":"Econometrica"},{"key":"2023031109460667900_","doi-asserted-by":"crossref","first-page":"447","DOI":"10.1214\/07-AIHP118","article-title":"Central limit theorems for eigenvalues in a spiked population model","volume":"44","author":"Bai","year":"2008","journal-title":"Ann. Inst. H. Poincar\u00e9"},{"key":"2023031109460667900_","doi-asserted-by":"crossref","first-page":"1382","DOI":"10.1016\/j.jmva.2005.08.003","article-title":"Eigenvalues of large sample covariance matrices of spiked population models","volume":"97","author":"Baik","year":"2006","journal-title":"J. Multiv. Anal."},{"key":"2023031109460667900_","doi-asserted-by":"crossref","first-page":"2577","DOI":"10.1214\/08-AOS600","article-title":"Covariance regularization by thresholding","volume":"36","author":"Bickel","year":"2008","journal-title":"Ann. Statist."},{"key":"2023031109460667900_","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":"2023031109460667900_","first-page":"696","article-title":"Structural shrinkage of nonparametric spectral estimators for multivariate time series","volume":"2","author":"Boehm","year":"2008","journal-title":"Electron. J. Statist."},{"key":"2023031109460667900_","doi-asserted-by":"crossref","first-page":"913","DOI":"10.1016\/j.jmva.2008.09.009","article-title":"Shrinkage estimation in the frequency domain of multivariate time series","volume":"100","author":"Boehm","year":"2009","journal-title":"J. Multiv. Anal."},{"key":"2023031109460667900_","doi-asserted-by":"crossref","first-page":"502","DOI":"10.1016\/j.csda.2007.02.009","article-title":"High-dimensional data clustering","volume":"52","author":"Bouveyron","year":"2007","journal-title":"Computnl Statist. Data Anal."},{"key":"2023031109460667900_","volume-title":"Alternating projections","author":"Boyd","year":"2003"},{"key":"2023031109460667900_","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511804441","volume-title":"Convex Optimization","author":"Boyd","year":"2004"},{"key":"2023031109460667900_","volume-title":"Time Series: Data Analysis and Theory","author":"Brillinger","year":"1981"},{"key":"2023031109460667900_","doi-asserted-by":"crossref","first-page":"577","DOI":"10.1080\/01621459.1998.10473711","article-title":"Nearest-neighbor clutter removal for estimating features in spatial point processes","volume":"93","author":"Byers","year":"1998","journal-title":"J. Am. Statist. Ass."},{"key":"2023031109460667900_","doi-asserted-by":"crossref","first-page":"672","DOI":"10.1198\/jasa.2011.tm10560","article-title":"Adaptive thresholding for sparse covariance matrix estimation","volume":"106","author":"Cai","year":"2011","journal-title":"J. Am. Statist. Ass."},{"key":"2023031109460667900_","doi-asserted-by":"crossref","first-page":"1438","DOI":"10.1198\/016214508000000869","article-title":"High-dimensional sparse factor modeling: applications in gene expression genomics","volume":"103","author":"Carvalho","year":"2008","journal-title":"J. Am. Statist. Ass."},{"key":"2023031109460667900_","doi-asserted-by":"crossref","first-page":"1305","DOI":"10.2307\/1912276","article-title":"Arbitrage, factor structure and mean-variance analysis in large asset markets","volume":"51","author":"Chamberlain","year":"1983","journal-title":"Econometrica"},{"key":"2023031109460667900_","doi-asserted-by":"crossref","first-page":"1405","DOI":"10.3150\/11-BEJ381","article-title":"Convergence of the largest eigenvalue of normalized sample covariance matrices when p and n both tend to infinity with their ratio converging to zero","volume":"18","author":"Chen","year":"2012","journal-title":"Bernoulli"},{"key":"2023031109460667900_","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1111\/j.1368-423X.2010.00330.x","article-title":"Weak and strong cross-section dependence and estimation of large panels","volume":"14","author":"Chudik","year":"2011","journal-title":"Econmetr. J."},{"key":"2023031109460667900_","doi-asserted-by":"crossref","first-page":"118","DOI":"10.1198\/108571101300325292","article-title":"Analysis of spatial point patterns using bundles product LISA function","volume":"6","author":"Collins","year":"2001","journal-title":"J. Agric. Biol. Environ. Statist."},{"key":"2023031109460667900_","volume-title":"GNU Octave Manual","author":"Eaton","year":"2002"},{"key":"2023031109460667900_","first-page":"117","article-title":"A comparison of three procedures for Robust PCA in high dimensions","volume":"34","author":"Engelen","year":"2005","journal-title":"Austn J. Statist."},{"key":"2023031109460667900_","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1016\/0304-405X(93)90023-5","article-title":"Common risk factors in the returns on stocks and bonds","volume":"33","author":"Fama","year":"1993","journal-title":"J. Finan. Econ."},{"key":"2023031109460667900_","doi-asserted-by":"crossref","first-page":"186","DOI":"10.1016\/j.jeconom.2008.09.017","article-title":"High dimensional covariance matrix estimation using a factor model","volume":"147","author":"Fan","year":"2008","journal-title":"J. Econmetr."},{"key":"2023031109460667900_","volume-title":"Estimation of false discovery proportion with unknown dependence","author":"Fan","year":"2013"},{"key":"2023031109460667900_","doi-asserted-by":"crossref","first-page":"3320","DOI":"10.1214\/11-AOS944","article-title":"High dimensional covariance matrix estimation in approximate factor models","volume":"39","author":"Fan","year":"2011","journal-title":"Ann. Statist."},{"key":"2023031109460667900_","doi-asserted-by":"crossref","first-page":"849","DOI":"10.1111\/j.1467-9868.2008.00674.x","article-title":"Sure independence screening for ultrahigh dimensional feature space (with discussion)","volume":"70","author":"Fan","year":"2008","journal-title":"J. R. Statist. Soc. B"},{"key":"2023031109460667900_","doi-asserted-by":"crossref","first-page":"592","DOI":"10.1080\/01621459.2012.682825","article-title":"Vast portfolio selection with gross-exposure constraints","volume":"107","author":"Fan","year":"2012","journal-title":"J. Am. Statist. Ass."},{"key":"2023031109460667900_","article-title":"Different estimators of the spectral matrix: an empirical comparison; testing a new shrinkage estimator","author":"Farn\u00e8","year":"2013","journal-title":"Communs Statist. Theor. Meth."},{"key":"2023031109460667900_","doi-asserted-by":"crossref","first-page":"540","DOI":"10.1162\/003465300559037","article-title":"The generalized dynamic factor model: identification and estimation","volume":"82","author":"Forni","year":"2000","journal-title":"Rev. Econ. Statist."},{"key":"2023031109460667900_","doi-asserted-by":"crossref","first-page":"231","DOI":"10.1016\/S0304-4076(03)00196-9","article-title":"The generalized dynamic factor model consistency and rates","volume":"119","author":"Forni","year":"2004","journal-title":"J. Econmetr."},{"key":"2023031109460667900_","doi-asserted-by":"crossref","first-page":"1113","DOI":"10.1017\/S0266466601176048","article-title":"The generalized dynamic factor model: representation theory","volume":"17","author":"Forni","year":"2001","journal-title":"Econmetr. Theor."},{"key":"2023031109460667900_","doi-asserted-by":"crossref","first-page":"531","DOI":"10.1126\/science.286.5439.531","article-title":"Molecular classification of cancer: class discovery and class prediction by gene expression monitoring","volume":"286","author":"Golub","year":"1999","journal-title":"Science"},{"key":"2023031109460667900_","doi-asserted-by":"crossref","first-page":"427","DOI":"10.1111\/j.1467-9868.2005.00510.x","article-title":"Geometric representation of high dimension, low sample size data","volume":"67","author":"Hall","year":"2005","journal-title":"J. R. Statist. Soc. B"},{"key":"2023031109460667900_","volume-title":"Statistical significance of clustering using soft thresholding","author":"Huang","year":"2013"},{"key":"2023031109460667900_","doi-asserted-by":"crossref","first-page":"1651","DOI":"10.1111\/1540-6261.00580","article-title":"Risk reduction in large portfolios: why imposing the wrong constraints helps","volume":"58","author":"Jagannathan","year":"2003","journal-title":"J. Finan."},{"key":"2023031109460667900_","doi-asserted-by":"crossref","first-page":"682","DOI":"10.1198\/jasa.2009.0121","article-title":"On consistency and sparsity for principal components analysis in high dimensions","volume":"104","author":"Johnstone","year":"2009","journal-title":"J. Am. Statist. Ass."},{"key":"2023031109460667900_","volume-title":"Principal Component Analysis","author":"Jolliffe","year":"2002"},{"key":"2023031109460667900_","doi-asserted-by":"crossref","first-page":"4104","DOI":"10.1214\/09-AOS709","article-title":"PCA consistency in high dimension, low sample size context","volume":"37","author":"Jung","year":"2009","journal-title":"Ann. Statist."},{"key":"2023031109460667900_","doi-asserted-by":"crossref","first-page":"196","DOI":"10.1016\/j.jmva.2012.03.005","article-title":"Boundary behavior in High Dimension, Low Sample Size asymptotics of PCA","volume":"109","author":"Jung","year":"2012","journal-title":"J. Multiv. Anal."},{"key":"2023031109460667900_","doi-asserted-by":"crossref","first-page":"2470","DOI":"10.1214\/11-AOAS489","article-title":"Efficient emulators of computer experiments using compactly supported correlation functions with an application to cosmology","volume":"5","author":"Kaufman","year":"2011","journal-title":"Ann. Appl. Statist."},{"key":"2023031109460667900_","doi-asserted-by":"crossref","first-page":"1545","DOI":"10.1198\/016214508000000959","article-title":"Covariance tapering for likelihood-based estimation in large spatial data sets","volume":"103","author":"Kaufman","year":"2008","journal-title":"J. Am. Statist. Ass."},{"key":"2023031109460667900_","volume-title":"Covariance assisted screening and estimation","author":"Ke","year":"2012"},{"key":"2023031109460667900_","doi-asserted-by":"crossref","first-page":"2522","DOI":"10.1016\/j.jbankfin.2012.05.005","article-title":"Parameter uncertainty in portfolio selection: shrinking the inverse covariance matrix","volume":"36","author":"Kourtis","year":"2012","journal-title":"J. Bankng Finan."},{"key":"2023031109460667900_","doi-asserted-by":"crossref","first-page":"694","DOI":"10.1214\/12-AOS970","article-title":"Factor modeling for high-dimensional time series: inference for the number of factors","volume":"40","author":"Lam","year":"2012","journal-title":"Ann. Statist."},{"key":"2023031109460667900_","doi-asserted-by":"crossref","first-page":"901","DOI":"10.1093\/biomet\/asr048","article-title":"Estimation of latent factors for high-dimensional time series","volume":"98","author":"Lam","year":"2011","journal-title":"Biometrika"},{"key":"2023031109460667900_","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1007\/s11222-008-9082-y","article-title":"Principal components analysis of nonstationary time series data","volume":"19","author":"Lansangan","year":"2009","journal-title":"Statist. Comput."},{"key":"2023031109460667900_","volume-title":"Factor Analysis as a Statistical Method","author":"Lawley","year":"1971"},{"key":"2023031109460667900_","doi-asserted-by":"crossref","first-page":"603","DOI":"10.1016\/S0927-5398(03)00007-0","article-title":"Improved estimation of the covariance matrix of stock returns with an application to portfolio selection","volume":"10","author":"Ledoit","year":"2003","journal-title":"J. Empir. Finan."},{"key":"2023031109460667900_","doi-asserted-by":"crossref","first-page":"365","DOI":"10.1016\/S0047-259X(03)00096-4","article-title":"A well-conditioned estimator for large-dimensional covariance matrices","volume":"88","author":"Ledoit","year":"2004","journal-title":"J. Multiv. Anal."},{"key":"2023031109460667900_","doi-asserted-by":"crossref","first-page":"2293","DOI":"10.1214\/12-AOS1037","article-title":"High dimensional semiparametric gaussian copula graphical models","volume":"40","author":"Liu","year":"2012","journal-title":"Ann. Statist."},{"key":"2023031109460667900_","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":"2023031109460667900_","volume-title":"Tiger: a tuning-insensitive approach for optimally estimating gaussian graphical models","author":"Liu","year":"2012"},{"key":"2023031109460667900_","first-page":"77","article-title":"Portfolio selection","volume":"7","author":"Markowitz","year":"1952","journal-title":"J. Finan."},{"key":"2023031109460667900_","doi-asserted-by":"crossref","first-page":"1447","DOI":"10.3982\/ECTA6964","article-title":"Testing hypotheses about the number of factors in large factor models","volume":"77","author":"Onatski","year":"2009","journal-title":"Econometrica"},{"key":"2023031109460667900_","doi-asserted-by":"crossref","first-page":"1004","DOI":"10.1162\/REST_a_00043","article-title":"Determining the number of factors from empirical distribution of eigenvalues","volume":"92","author":"Onatski","year":"2010","journal-title":"Rev. Econ. Statist."},{"key":"2023031109460667900_","volume-title":"Posterior contraction in sparse Bayesian factor models for massive covariance matrices","author":"Pati","year":"2012"},{"key":"2023031109460667900_","first-page":"1617","article-title":"Asymptotics of sample eigenstructure for a large dimensional spiked covariance model","volume":"17","author":"Paul","year":"2007","journal-title":"Statist. Sin."},{"key":"2023031109460667900_","volume-title":"Testing CAPM with a large number of assets","author":"Pesaran","year":"2012"},{"key":"2023031109460667900_","doi-asserted-by":"crossref","DOI":"10.1002\/9781118573617","volume-title":"High-dimensional Covariance Estimation","author":"Pourahmadi","year":"2013"},{"key":"2023031109460667900_","article-title":"A shrinkage approach to large-scale covariance matrix estimation and implications for functional genomics","volume":"4","author":"Schaefer","year":"2005","journal-title":"Statist. Applic. Genet. Molec. Biol."},{"key":"2023031109460667900_","article-title":"A general framework for consistency of principal component analysis","author":"Shen","year":"2012","journal-title":"Preprint arXiv:1211.2671"},{"key":"2023031109460667900_","doi-asserted-by":"crossref","first-page":"317","DOI":"10.1016\/j.jmva.2012.10.007","article-title":"Consistency of sparse PCA in high dimension, low sample size contexts","volume":"115","author":"Shen","year":"2013","journal-title":"J. Multiv. Anal."},{"key":"2023031109460667900_","doi-asserted-by":"crossref","first-page":"147","DOI":"10.1198\/073500102317351921","article-title":"Macroeconomic forecasting using diffusion indexes","volume":"20","author":"Stock","year":"2002","journal-title":"J. Bus. Econ. Statist."},{"key":"2023031109460667900_","doi-asserted-by":"crossref","first-page":"1167","DOI":"10.1198\/016214502388618960","article-title":"Forecasting using principal components from a large number of predictors","volume":"97","author":"Stock","year":"2002","journal-title":"J. Am. Statist. Ass."},{"key":"2023031109460667900_","doi-asserted-by":"crossref","DOI":"10.3386\/w11467","volume-title":"Implications of dynamic factor models for VAR analysis","author":"Stock","year":"2005"},{"key":"2023031109460667900_","volume-title":"Precision matrix estimation by inverse principle orthogonal decomposition","author":"Tang","year":"2013"},{"key":"2023031109460667900_","doi-asserted-by":"crossref","first-page":"549","DOI":"10.1111\/j.1467-9868.2009.00706.x","article-title":"Invariant co-ordinate selection (with discussion)","volume":"71","author":"Tyler","year":"2009","journal-title":"J. R. Statist. Soc. B"},{"key":"2023031109460667900_","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1093\/biomet\/asr074","article-title":"Factor profiled sure independence screening","volume":"99","author":"Wang","year":"2012","journal-title":"Biometrika"},{"key":"2023031109460667900_","doi-asserted-by":"crossref","first-page":"427","DOI":"10.1111\/j.1467-9868.2012.01049.x","article-title":"Condition-number-regularized covariance estimation","volume":"75","author":"Won","year":"2013","journal-title":"J. R. Statist. Soc. B"},{"key":"2023031109460667900_","doi-asserted-by":"crossref","first-page":"1480","DOI":"10.1080\/01621459.2012.725386","article-title":"Positive definite l1 penalized estimation of large covariance matrices","volume":"107","author":"Xue","year":"2012","journal-title":"J. Am. Statist. Ass."},{"key":"2023031109460667900_","doi-asserted-by":"crossref","DOI":"10.2139\/ssrn.1950239","volume-title":"Sparse weighted norm minimum variance portfolio","author":"Yen","year":"2011"},{"key":"2023031109460667900_","doi-asserted-by":"crossref","first-page":"3771","DOI":"10.1093\/bioinformatics\/bti604","article-title":"Two-stage designs for experiments with a large number of hypotheses","volume":"21","author":"Zehetmayer","year":"2005","journal-title":"Bioinformatics"},{"key":"2023031109460667900_","doi-asserted-by":"crossref","first-page":"4145","DOI":"10.1002\/sim.3300","article-title":"Optimized multi-stage designs controlling the false discovery or the family-wise error rate","volume":"27","author":"Zehetmayer","year":"2008","journal-title":"Statist. Med."},{"key":"2023031109460667900_","volume-title":"Source screening for neuroimaging","author":"Zhang","year":"2012"},{"key":"2023031109460667900_","volume-title":"Source localization with MEG data","author":"Zhang","year":"2012"}],"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%2Frssb.12016","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/academic.oup.com\/jrsssb\/article-pdf\/75\/4\/603\/49507152\/jrsssb_75_4_603.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/jrsssb\/article-pdf\/75\/4\/603\/49507152\/jrsssb_75_4_603.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,7,3]],"date-time":"2023-07-03T16:34:19Z","timestamp":1688402059000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/jrsssb\/article\/75\/4\/603\/7075932"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,8,12]]},"references-count":147,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2013,8,12]]},"published-print":{"date-parts":[[2013,9,1]]}},"URL":"https:\/\/doi.org\/10.1111\/rssb.12016","relation":{},"ISSN":["1369-7412","1467-9868"],"issn-type":[{"value":"1369-7412","type":"print"},{"value":"1467-9868","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2013,9]]},"published":{"date-parts":[[2013,8,12]]}}}