2,194
Views
111
CrossRef citations to date
0
Altmetric
Theory and Methods

Positive-Definite ℓ1-Penalized Estimation of Large Covariance Matrices

, &
Pages 1480-1491 | Received 01 Nov 2011, Published online: 21 Dec 2012

Keep up to date with the latest research on this topic with citation updates for this article.

Read on this site (23)

Danning Li, Arun Srinivasan, Qian Chen & Lingzhou Xue. (2023) Robust Covariance Matrix Estimation for High-Dimensional Compositional Data with Application to Sales Data Analysis. Journal of Business & Economic Statistics 41:4, pages 1090-1100.
Read now
Wenyu Yang & Xiaoning Kang. (2023) An improved banded estimation for large covariance matrix. Communications in Statistics - Theory and Methods 52:1, pages 141-155.
Read now
Xiao Liu, Chungen Shen & Li Wang. (2022) A dual active-set proximal Newton algorithm for sparse approximation of correlation matrices. Optimization Methods and Software 37:5, pages 1820-1844.
Read now
Chunshi Li, Mo Yang, Mingqiu Wang, Hong Kang & Xiaoning Kang. (2021) A Cholesky-based sparse covariance estimation with an application to genes data. Journal of Biopharmaceutical Statistics 31:5, pages 603-616.
Read now
Shaoxin Wang & Hu Yang. (2021) Conditioning theory of the equality constrained quadratic programming and its applications. Linear and Multilinear Algebra 69:6, pages 1161-1183.
Read now
Zheng Tracy Ke, Lingzhou Xue & Fan Yang. (2020) Diagonally Dominant Principal Component Analysis. Journal of Computational and Graphical Statistics 29:3, pages 592-607.
Read now
Xiaoning Kang, Chaoping Xie & Mingqiu Wang. (2020) A Cholesky-based estimation for large-dimensional covariance matrices. Journal of Applied Statistics 47:6, pages 1017-1030.
Read now
Wei Qian, Shanshan Ding & R. Dennis Cook. (2019) Sparse Minimum Discrepancy Approach to Sufficient Dimension Reduction with Simultaneous Variable Selection in Ultrahigh Dimension. Journal of the American Statistical Association 114:527, pages 1277-1290.
Read now
Young-Geun Choi, Johan Lim & Sujung Choi. (2019) High-dimensional Markowitz portfolio optimization problem: empirical comparison of covariance matrix estimators. Journal of Statistical Computation and Simulation 89:7, pages 1278-1300.
Read now
Jacob Bien. (2019) Graph-Guided Banding of the Covariance Matrix. Journal of the American Statistical Association 114:526, pages 782-792.
Read now
Yuwen Gu, Jun Fan, Lingchen Kong, Shiqian Ma & Hui Zou. (2018) ADMM for High-Dimensional Sparse Penalized Quantile Regression. Technometrics 60:3, pages 319-331.
Read now
Vahe Avagyan, Andrés M. Alonso & Francisco J. Nogales. (2017) Improving the Graphical Lasso Estimation for the Precision Matrix Through Roots of the Sample Covariance Matrix. Journal of Computational and Graphical Statistics 26:4, pages 865-872.
Read now
Brett Naul & Jonathan Taylor. (2017) Sparse Steinian Covariance Estimation. Journal of Computational and Graphical Statistics 26:2, pages 355-366.
Read now
Hao Zheng, Kam-Wah Tsui, Xiaoning Kang & Xinwei Deng. (2017) Cholesky-based model averaging for covariance matrix estimation. Statistical Theory and Related Fields 1:1, pages 48-58.
Read now
Tao Zou, Wei Lan, Hansheng Wang & Chih-Ling Tsai. (2017) Covariance Regression Analysis. Journal of the American Statistical Association 112:517, pages 266-281.
Read now
Jianqing Fan, Lingzhou Xue & Hui Zou. (2016) Multitask Quantile Regression Under the Transnormal Model. Journal of the American Statistical Association 111:516, pages 1726-1735.
Read now
Ziqi Chen & Chenlei Leng. (2016) Dynamic Covariance Models. Journal of the American Statistical Association 111:515, pages 1196-1207.
Read now
Yixin Fang, Binhuan Wang & Yang Feng. (2016) Tuning-parameter selection in regularized estimations of large covariance matrices. Journal of Statistical Computation and Simulation 86:3, pages 494-509.
Read now
Yafei Huang & Peter M. Bentler. (2015) Behavior of Asymptotically Distribution Free Test Statistics in Covariance Versus Correlation Structure Analysis. Structural Equation Modeling: A Multidisciplinary Journal 22:4, pages 489-503.
Read now
S.-M. Chang. (2015) Double shrinkage estimators for large sparse covariance matrices. Journal of Statistical Computation and Simulation 85:8, pages 1497-1511.
Read now
Heng Lian & Zengyan Fan. (2015) Estimation of a sparse and spiked covariance matrix. Journal of Nonparametric Statistics 27:2, pages 241-252.
Read now
Han Liu, Lie Wang & Tuo Zhao. (2014) Sparse Covariance Matrix Estimation With Eigenvalue Constraints. Journal of Computational and Graphical Statistics 23:2, pages 439-459.
Read now
Arkajyoti Saha, Daniela Witten & Jacob Bien. Inferring independent sets of Gaussian variables after thresholding correlations. Journal of the American Statistical Association 0:0, pages 1-20.
Read now

Articles from other publishers (88)

Xin Wang, Lingchen Kong & Liqun Wang. (2024) Estimation of sparse covariance matrix via non-convex regularization. Journal of Multivariate Analysis 202, pages 105294.
Crossref
Wan Tian & Zhongfeng Qin. (2024) The minimum covariance determinant estimator for interval-valued data. Statistics and Computing 34:2.
Crossref
Xiufan Yu, Jiawei Yao & Lingzhou Xue. (2024) Power enhancement for testing multi-factor asset pricing models via Fisher’s method. Journal of Econometrics 239:2, pages 105458.
Crossref
Aaron J. Molstad, Karl Oskar Ekvall & Piotr M. Suder. (2024) Direct covariance matrix estimation with compositional data. Electronic Journal of Statistics 18:1.
Crossref
Ghania Fatima, Prabhu Babu & Petre Stoica. (2024) Two New Algorithms for Maximum Likelihood Estimation of Sparse Covariance Matrices With Applications to Graphical Modeling. IEEE Transactions on Signal Processing 72, pages 958-971.
Crossref
Reza Mirzaeifard, Naveen K. D. Venkategowda, Vinay Chakravarthi Gogineni & Stefan Werner. (2024) Smoothing ADMM for Sparse-Penalized Quantile Regression With Non-Convex Penalties. IEEE Open Journal of Signal Processing 5, pages 213-228.
Crossref
Liyuan Cui, Yongmiao Hong, Yingxing Li & Junhui Wang. (2023) A Regularized High-Dimensional Positive Definite Covariance Estimator with High-Frequency Data. Management Science.
Crossref
Zhenguo Gao, Xinye Wang & Xiaoning Kang. (2023) Ensemble LDA via the modified Cholesky decomposition. Computational Statistics & Data Analysis 188, pages 107823.
Crossref
Song Xi Chen, Yumou Qiu & Shuyi Zhang. (2023) Sharp optimality for high-dimensional covariance testing under sparse signals. The Annals of Statistics 51:5.
Crossref
Rakheon Kim, Mohsen Pourahmadi & Tanya P. Garcia. (2023) Positive-definite thresholding estimators of covariance matrices with zeros. Journal of Multivariate Analysis 197, pages 105186.
Crossref
Song Xi Chen, Bin Guo & Yumou Qiu. (2023) Testing and signal identification for two-sample high-dimensional covariances via multi-level thresholding. Journal of Econometrics 235:2, pages 1337-1354.
Crossref
Reza Mirzaeifard, Vinay Chakravarthi Gogineni, Naveen K. D. Venkategowda & Stefan Werner. (2023) Distributed Quantile Regression with Non-Convex Sparse Penalties. Distributed Quantile Regression with Non-Convex Sparse Penalties.
Wenfu Xia, Ziping Zhao & Ying Sun. (2023) C-ISTA: Iterative Shrinkage-Thresholding Algorithm for Sparse Covariance Matrix Estimation. C-ISTA: Iterative Shrinkage-Thresholding Algorithm for Sparse Covariance Matrix Estimation.
Quan Wei & Ziping Zhao. (2023) Large Covariance Matrix Estimation with Oracle Statistical Rate. Large Covariance Matrix Estimation with Oracle Statistical Rate.
Huiqin Xin & Sihai Dave Zhao. (2023) A Compound Decision Approach to Covariance Matrix Estimation. Biometrics 79:2, pages 1201-1212.
Crossref
Xin Wang, Lingchen Kong, Liqun Wang & Zhaoqilin Yang. (2023) High-Dimensional Covariance Estimation via Constrained Lq-Type Regularization. Mathematics 11:4, pages 1022.
Crossref
Quan Wei & Ziping Zhao. (2023) Large Covariance Matrix Estimation With Oracle Statistical Rate via Majorization-Minimization. IEEE Transactions on Signal Processing 71, pages 3328-3342.
Crossref
Xiaoning Kang, Zhiyang Zhang & Xinwei Deng. 2023. Springer Handbook of Engineering Statistics. Springer Handbook of Engineering Statistics 887 900 .
Jing Guo, Yu Guo, Qiyu Jin, Michael Kwok-Po Ng & Shuping Wang. (2022) Gaussian Patch Mixture Model Guided Low-Rank Covariance Matrix Minimization for Image Denoising. SIAM Journal on Imaging Sciences 15:4, pages 1601-1622.
Crossref
Jason Xu & Kenneth Lange. (2022) A proximal distance algorithm for likelihood-based sparse covariance estimation. Biometrika 109:4, pages 1047-1066.
Crossref
Yan Zhang, Jiyuan Tao, Zhixiang Yin & Guoqiang Wang. (2022) Improved Large Covariance Matrix Estimation Based on Efficient Convex Combination and Its Application in Portfolio Optimization. Mathematics 10:22, pages 4282.
Crossref
Seyoon Ko, Hua Zhou, Jin J. Zhou & Joong-Ho Won. (2022) High-Performance Statistical Computing in the Computing Environments of the 2020s. Statistical Science 37:4.
Crossref
Reza Mirzaeifard, Naveen K. D. Venkategowda, Vinay Chakravarthi Gogineni & Stefan Werner. (2022) ADMM for Sparse-Penalized Quantile Regression with Non-Convex Penalties. ADMM for Sparse-Penalized Quantile Regression with Non-Convex Penalties.
Necdet Serhat Aybat, Hesam Ahmadi & Uday V. Shanbhag. (2022) On the Analysis of Inexact Augmented Lagrangian Schemes for Misspecified Conic Convex Programs. IEEE Transactions on Automatic Control 67:8, pages 3981-3996.
Crossref
Wei Luo, Lingzhou Xue, Jiawei Yao & Xiufan Yu. (2022) Inverse moment methods for sufficient forecasting using high-dimensional predictors. Biometrika 109:2, pages 473-487.
Crossref
Kensuke Tanioka, Yuki Furotani & Satoru Hiwa. (2022) Thresholding Approach for Low-Rank Correlation Matrix Based on MM Algorithm. Entropy 24:5, pages 579.
Crossref
Lin XIA, Guanpeng WANG & Xudong HUANG. (2022) ADMM Algorithmic Regularization Paths for Sparse and Large Scale Positive-Definite Covariance Matrix Estimation. Wuhan University Journal of Natural Sciences 27:2, pages 128-134.
Crossref
Jiaying Weng. (2022) Fourier transform sparse inverse regression estimators for sufficient variable selection. Computational Statistics & Data Analysis 168, pages 107380.
Crossref
Sijia Yang, Haoyi Xiong, Yunchao Zhang, Yi Ling, Licheng Wang, Kaibo Xu & Zeyi Sun. (2021) OGM: Online gaussian graphical models on the fly. Applied Intelligence 52:3, pages 3103-3117.
Crossref
Jie Chen, Ryosuke Shimmura & Joe Suzuki. (2021) Efficient Proximal Gradient Algorithms for Joint Graphical Lasso. Entropy 23:12, pages 1623.
Crossref
Seonghun Cho, Shota Katayama, Johan Lim & Young-Geun Choi. (2021) Positive-definite modification of a covariance matrix by minimizing the matrix $$\ell_{\infty}$$ norm with applications to portfolio optimization. AStA Advances in Statistical Analysis 105:4, pages 601-627.
Crossref
Adam B. Kashlak & Linglong Kong. (2021) Nonasymptotic support recovery for high‐dimensional sparse covariance matrices. Stat 10:1.
Crossref
Hoai An Le Thi, Duy Nhat Phan & Tao Pham Dinh. (2021) DCA based approaches for bi-level variable selection and application for estimate multiple sparse covariance matrices. Neurocomputing 466, pages 162-177.
Crossref
Xuefeng Li & Xiuli Liu. (2021) Identifying Hub Wastewater Propagation Chains in China’s National Economic System: A Model Coupled Input-Output Analysis with Graphical Theory. Water 13:17, pages 2351.
Crossref
Junwei Lu, Fang Han & Han Liu. (2021) Robust Scatter Matrix Estimation for High Dimensional Distributions With Heavy Tail. IEEE Transactions on Information Theory 67:8, pages 5283-5304.
Crossref
Fei Wen, Lei Chu, Rendong Ying & Peilin Liu. (2021) Fast and Positive Definite Estimation of Large Covariance Matrix for High-Dimensional Data Analysis. IEEE Transactions on Big Data 7:3, pages 603-609.
Crossref
Yihe Yang, Jie Zhou & Jianxin Pan. (2021) Estimation and optimal structure selection of high-dimensional Toeplitz covariance matrix. Journal of Multivariate Analysis 184, pages 104739.
Crossref
Xiaoning Kang & Mingqiu Wang. (2021) Ensemble sparse estimation of covariance structure for exploring genetic disease data. Computational Statistics & Data Analysis 159, pages 107220.
Crossref
Xiaoning Kang & Xinwei Deng. (2020) On variable ordination of Cholesky‐based estimation for a sparse covariance matrix. Canadian Journal of Statistics 49:2, pages 283-310.
Crossref
Shaoxin Wang. (2021) An efficient numerical method for condition number constrained covariance matrix approximation. Applied Mathematics and Computation 397, pages 125925.
Crossref
Yang Xu, Arun Srinivasan & Lingzhou Xue. 2021. Modern Statistical Methods for Health Research. Modern Statistical Methods for Health Research 247 277 .
Jin Hyun Nam, Donguk Kim & Dongjun Chung. (2020) Sparse linear discriminant analysis using the prior-knowledge-guided block covariance matrix. Chemometrics and Intelligent Laboratory Systems 206, pages 104142.
Crossref
Yilei Wu, Yingli Qin & Mu Zhu. (2019) High‐dimensional covariance matrix estimation using a low‐rank and diagonal decomposition. Canadian Journal of Statistics 48:2, pages 308-337.
Crossref
Clifford Lam. (2019) High‐dimensional covariance matrix estimation. WIREs Computational Statistics 12:2.
Crossref
Abhirup Datta, Sudipto Banerjee, James S. Hodges & Leiwen Gao. (2019) Spatial Disease Mapping Using Directed Acyclic Graph Auto-Regressive (DAGAR) Models. Bayesian Analysis 14:4.
Crossref
Guangren Yang, Yiming Liu & Guangming Pan. (2019) Weighted covariance matrix estimation. Computational Statistics & Data Analysis 139, pages 82-98.
Crossref
Shaoxin Wang, Hu Yang & Chaoli Yao. (2019) On the penalized maximum likelihood estimation of high-dimensional approximate factor model. Computational Statistics 34:2, pages 819-846.
Crossref
Young-Geun Choi, Johan Lim, Anindya Roy & Junyong Park. (2019) Fixed support positive-definite modification of covariance matrix estimators via linear shrinkage. Journal of Multivariate Analysis 171, pages 234-249.
Crossref
Misagh Khayambashi & Arnold Lee Swindlehurst. (2019) Estimation of Sparse Directional Connectivity With Expectation Maximization. IEEE Transactions on Signal Processing 67:4, pages 854-869.
Crossref
Natalia Bailey, M. Hashem Pesaran & L. Vanessa Smith. (2019) A multiple testing approach to the regularisation of large sample correlation matrices. Journal of Econometrics 208:2, pages 507-534.
Crossref
Xiangzhao Cui, Zhenyang Li, Jine Zhao, Defei Zhang & Jianxin Pan. 2019. Matrices, Statistics and Big Data. Matrices, Statistics and Big Data 111 125 .
Arnab Chakrabarti & Rituparna Sen. 2019. New Perspectives and Challenges in Econophysics and Sociophysics. New Perspectives and Challenges in Econophysics and Sociophysics 147 167 .
Chenlei Leng & Guangming Pan. (2018) Covariance estimation via sparse Kronecker structures. Bernoulli 24:4B.
Crossref
Zhihong Jian, Pingjun Deng & Zhican Zhu. (2018) High-dimensional covariance forecasting based on principal component analysis of high-frequency data. Economic Modelling 75, pages 422-431.
Crossref
Aaron J Molstad & Adam J Rothman. (2018) Shrinking characteristics of precision matrix estimators. Biometrika 105:3, pages 563-574.
Crossref
Vahe Avagyan, Andrés M. Alonso & Francisco J. Nogales. (2016) D-trace estimation of a precision matrix using adaptive Lasso penalties. Advances in Data Analysis and Classification 12:2, pages 425-447.
Crossref
Fei Wen, Lei Chu, Peilin Liu & Robert C. Qiu. (2018) A Survey on Nonconvex Regularization-Based Sparse and Low-Rank Recovery in Signal Processing, Statistics, and Machine Learning. IEEE Access 6, pages 69883-69906.
Crossref
Jianbo Li, Jie Zhou & Bin Zhang. (2018) Estimation of Large Covariance Matrices by Shrinking to Structured Target in Normal and Non-Normal Distributions. IEEE Access 6, pages 2158-2169.
Crossref
Duy Nhat Phan, Hoai An Le Thi & Tao Pham Dinh. (2017) Sparse Covariance Matrix Estimation by DCA-Based Algorithms. Neural Computation 29:11, pages 3040-3077.
Crossref
Philip L.H. Yu, Xiaohang Wang & Yuanyuan Zhu. (2017) High dimensional covariance matrix estimation by penalizing the matrix-logarithm transformed likelihood. Computational Statistics & Data Analysis 114, pages 12-25.
Crossref
Hailin Sun & Qiyu Wang. (2017) Sparse Markowitz portfolio selection by using stochastic linear complementarity approach. Journal of Industrial and Management Optimization 13:2, pages 59-59.
Crossref
Haoyi Xiong, Jinghe Zhang, Yu Huang, Kevin Leach & Laura E. Barnes. (2017) Daehr . ACM Transactions on Intelligent Systems and Technology 8:3, pages 1-21.
Crossref
Zekai J. Gao & Chris Jermaine. (2016) Distributed Algorithms for Computing Very Large Thresholded Covariance Matrices. ACM Transactions on Knowledge Discovery from Data 11:2, pages 1-25.
Crossref
Jasper Engel, Lutgarde Buydens & Lionel Blanchet. (2017) An overview of large‐dimensional covariance and precision matrix estimators with applications in chemometrics. Journal of Chemometrics 31:4.
Crossref
Abdelkader Baggag, Halima Bensmail & Jaideep Srivastava. 2017. Advances in Knowledge Discovery and Data Mining. Advances in Knowledge Discovery and Data Mining 27 38 .
Gongjun Xu, Lifeng Lin, Peng Wei & Wei Pan. (2016) An adaptive two-sample test for high-dimensional means. Biometrika 103:3, pages 609-624.
Crossref
Peng WangJianhui ZhouAnnie Qu. (2016) Correlation structure selection for longitudinal data with diverging cluster size. Canadian Journal of Statistics 44:3, pages 343-360.
Crossref
Shiqian Ma. (2015) Alternating Proximal Gradient Method for Convex Minimization. Journal of Scientific Computing 68:2, pages 546-572.
Crossref
Marten Wegkamp & Yue Zhao. (2016) Adaptive estimation of the copula correlation matrix for semiparametric elliptical copulas. Bernoulli 22:2.
Crossref
Jianqing Fan, Yuan Liao & Han Liu. 2016. Financial Signal Processing and Machine Learning. Financial Signal Processing and Machine Learning 100 134 .
Jushan Bai & Yuan Liao. (2016) Efficient estimation of approximate factor models via penalized maximum likelihood. Journal of Econometrics 191:1, pages 1-18.
Crossref
Xiangzhao Cui, Chun Li, Jine Zhao, Li Zeng, Defei Zhang & Jianxin Pan. (2016) Regularization for high-dimensional covariance matrix. Special Matrices 4:1.
Crossref
Fei Wen, Yuan Yang, Peilin Liu & Robert C. Qiu. (2016) Positive definite estimation of large covariance matrix using generalized nonconvex penalties. IEEE Access 4, pages 4168-4182.
Crossref
Ying Cui, Chenlei Leng & Defeng Sun. (2016) Sparse estimation of high-dimensional correlation matrices. Computational Statistics & Data Analysis 93, pages 390-403.
Crossref
Sheng-Long Zhou, Nai-Hua Xiu, Zi-Yan Luo & Ling-Chen Kong. (2014) Sparse and Low-Rank Covariance Matrix Estimation. Journal of the Operations Research Society of China 3:2, pages 231-250.
Crossref
Kofi P. Adragni & Moumita Karmakar. (2015) A sequential test for variable selection in high dimensional complex data. Computational Statistics & Data Analysis 81, pages 107-120.
Crossref
Wenbao Yu & Taesung Park. (2014) AucPR: An AUC-based approach using penalized regression for disease prediction with high-dimensional omics data. BMC Genomics 15:S10.
Crossref
Kenneth Lange, Eric C. Chi & Hua Zhou. (2014) A Brief Survey of Modern Optimization for Statisticians. International Statistical Review 82:1, pages 46-70.
Crossref
Feng Ma, Mingfang Ni, Lei Zhu & Zhanke Yu. (2014) An Implementable First-Order Primal-Dual Algorithm for Structured Convex Optimization. Abstract and Applied Analysis 2014, pages 1-9.
Crossref
M. Ross Kunz & Yiyuan She. (2013) Multivariate calibration maintenance and transfer through robust fused LASSO. Journal of Chemometrics 27:9, pages 233-242.
Crossref
Shiqian Ma, Lingzhou XueHui Zou. (2013) Alternating Direction Methods for Latent Variable Gaussian Graphical Model Selection. Neural Computation 25:8, pages 2172-2198.
Crossref
Mohsen Pourahmadi. 2013. High‐Dimensional Covariance Estimation. High‐Dimensional Covariance Estimation 171 179 .
Jianqing Fan & Han Liu. (2013) Statistical analysis of big data on pharmacogenomics. Advanced Drug Delivery Reviews 65:7, pages 987-1000.
Crossref
Liyuan Cui, Yongmiao Hong, Yingxing Li & Junhui Wang. (2019) A Machine Learning Approach to Estimating Large Positive Definite Covariance Matrix of High Frequency Data. SSRN Electronic Journal.
Crossref
Qiyu Wang & Hui Shao. (2017) Sparse Markowitz Portfolio Selection by Penalty Methods. SSRN Electronic Journal.
Crossref
Wei Luo, Lingzhou Xue & Jiawei Yao. (2016) Inverse Moment Methods for Sufficient Forecasting Using High-Dimensional Predictors. SSRN Electronic Journal.
Crossref
Tao Zou, Wei Lan, Hansheng Wang & Chih-Ling Tsai. (2015) Covariance Regression Analysis. SSRN Electronic Journal.
Crossref
Jushan Bai & Yuan Liao. (2013) Statistical Inferences Using Large Estimated Covariances for Panel Data and Factor Models. SSRN Electronic Journal.
Crossref

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.