메뉴 건너뛰기




Volumn 5, Issue , 2011, Pages 935-980

High-dimensional covariance estimation by minimizing ℓ 1-penalized log-determinant divergence

Author keywords

1 regularization; Concentration; Covariance; Gaussian graphical models; Precision; Sparsity

Indexed keywords


EID: 80555142374     PISSN: 19357524     EISSN: None     Source Type: Journal    
DOI: 10.1214/11-EJS631     Document Type: Article
Times cited : (757)

References (33)
  • 1
    • 62349112885 scopus 로고    scopus 로고
    • Covariance regularization by thresholding
    • P. J. Bickel and E. Levina. Covariance regularization by thresholding. Ann. Statist., 36(6):2577-2604, 2008.
    • (2008) Ann. Statist , vol.36 , Issue.6 , pp. 2577-2604
    • Bickel, P.J.1    Levina, E.2
  • 2
    • 41549106844 scopus 로고    scopus 로고
    • Regularized estimation of large covariance matrices
    • P. J. Bickel and E. Levina. Regularized estimation of large covariance matrices. Ann. Statist., 36(1):199-227, 2008.
    • (2008) Ann. Statist , vol.36 , Issue.1 , pp. 199-227
    • Bickel, P.J.1    Levina, E.2
  • 4
    • 0040478203 scopus 로고
    • The relaxation method for finding the common point of convex sets and its application to the solution of problems in convex programming
    • L. M. Bregman. The relaxation method for finding the common point of convex sets and its application to the solution of problems in convex programming. USSR Computational Mathematics and Mathematical Physics, 7:191-204, 1967.
    • (1967) USSR Computational Mathematics and Mathematical Physics , vol.7 , pp. 191-204
    • Bregman, L.M.1
  • 7
    • 77955132618 scopus 로고    scopus 로고
    • Optimal rates of convergence for covariance matrix estimation
    • To appear
    • T. T. Cai, C.-H. Zhang, and H. H. Zhou. Optimal rates of convergence for covariance matrix estimation. Annals of Statistics, 2010. To appear.
    • (2010) Annals of Statistics
    • Cai, T.T.1    Zhang, C.-H.2    Zhou, H.H.3
  • 10
    • 62349123505 scopus 로고    scopus 로고
    • Operator norm consistent estimation of large dimensional sparse covariance matrices
    • To appear
    • N. El Karoui. Operator norm consistent estimation of large dimensional sparse covariance matrices. Ann. Statist., To appear, 2008.
    • (2008) Ann. Statist
    • El Karoui, N.1
  • 11
    • 45849134070 scopus 로고    scopus 로고
    • Sparse inverse covariance estimation with the graphical Lasso
    • J. Friedman, T. Hastie, and R. Tibshirani. Sparse inverse covariance estimation with the graphical Lasso. Biostat., 9(3):432-441, 2007.
    • (2007) Biostat , vol.9 , Issue.3 , pp. 432-441
    • Friedman, J.1    Hastie, T.2    Tibshirani, R.3
  • 12
    • 33750502680 scopus 로고    scopus 로고
    • Estimation of high-dimensional prior and posterior covariance matrices in kalman filter variants
    • R. Furrer and T. Bengtsson. Estimation of high-dimensional prior and posterior covariance matrices in kalman filter variants. J. Multivar. Anal., 98(2):227-255, 2007.
    • (2007) J. Multivar. Anal , vol.98 , Issue.2 , pp. 227-255
    • Furrer, R.1    Bengtsson, T.2
  • 13
    • 85017322137 scopus 로고    scopus 로고
    • Estimation of gaussian graph by model selection
    • C. Giraud. Estimation of gaussian graph by model selection. Electronic Journal of Statistics, 2:542-563, 2008.
    • (2008) Electronic Journal of Statistics , vol.2 , pp. 542-563
    • Giraud, C.1
  • 15
    • 33644986127 scopus 로고    scopus 로고
    • Covariance matrix selection and estimation via penalised normal likelihood
    • J. Z. Huang, N. Liu, M. Pourahmadi, and L. Liu. Covariance matrix selection and estimation via penalised normal likelihood. Biometrika, 93(1):85-98, 2006.
    • (2006) Biometrika , vol.93 , Issue.1 , pp. 85-98
    • Huang, J.Z.1    Liu, N.2    Pourahmadi, M.3    Liu, L.4
  • 16
    • 0035641726 scopus 로고    scopus 로고
    • On the distribution of the largest eigenvalue in principal components analysis
    • I. M. Johnstone. On the distribution of the largest eigenvalue in principal components analysis. Ann. Statist., 29(2):295-327, 2001.
    • (2001) Ann. Statist , vol.29 , Issue.2 , pp. 295-327
    • Johnstone, I.M.1
  • 18
    • 73949122606 scopus 로고    scopus 로고
    • Sparsistency and rates of convergence in large covariance matrix estimation
    • C. Lam and J. Fan. Sparsistency and rates of convergence in large covariance matrix estimation. Annals of Statistics, 37:4254-4278, 2009.
    • (2009) Annals of Statistics , vol.37 , pp. 4254-4278
    • Lam, C.1    Fan, J.2
  • 19
    • 0346961488 scopus 로고    scopus 로고
    • A well-conditioned estimator for largedimensional covariance matrices
    • O. Ledoit and M. Wolf. A well-conditioned estimator for largedimensional covariance matrices. J. Multivar. Anal., 88:365-411, 2003.
    • (2003) J. Multivar. Anal , vol.88 , pp. 365-411
    • Ledoit, O.1    Wolf, M.2
  • 20
    • 0038609707 scopus 로고    scopus 로고
    • Mathematical Surveys and Monographs. American Mathematical Society, Providence, RI
    • M. Ledoux. The Concentration of Measure Phenomenon. Mathematical Surveys and Monographs. American Mathematical Society, Providence, RI, 2001.
    • (2001) The Concentration of Measure Phenomenon
    • Ledoux, M.1
  • 21
    • 42649092921 scopus 로고    scopus 로고
    • A note on the Lasso for graphical Gaussian model selection
    • N. Meinshausen. A note on the Lasso for graphical Gaussian model selection. Statistics and Probability Letters, 78(7): 880-884, 2008.
    • (2008) Statistics and Probability Letters , vol.78 , Issue.7 , pp. 880-884
    • Meinshausen, N.1
  • 22
    • 33747163541 scopus 로고    scopus 로고
    • High-dimensional graphs and variable selection with the Lasso
    • N. Meinshausen and P. Bühlmann. High-dimensional graphs and variable selection with the Lasso. Ann. Statist., 34(3):1436-1462, 2006.
    • (2006) Ann. Statist , vol.34 , Issue.3 , pp. 1436-1462
    • Meinshausen, N.1    Bühlmann, P.2
  • 26
    • 51249187914 scopus 로고
    • p (p > 2) spanned by sequences of independent random variables
    • p (p > 2) spanned by sequences of independent random variables. Israel J. Math, 8:1546-1570, 1970.
    • (1970) Srael J. Math , vol.8 , pp. 1546-1570
    • Rosenthal, H.P.1
  • 28
    • 33645712308 scopus 로고    scopus 로고
    • Just relax: Convex programming methods for identifying sparse signals
    • J. A. Tropp. Just relax: Convex programming methods for identifying sparse signals. IEEE Trans. Info. Theory, 51(3): 1030-1051, 2006.
    • (2006) IEEE Trans. Info. Theory , vol.51 , Issue.3 , pp. 1030-1051
    • Tropp, J.A.1
  • 29
    • 65749083666 scopus 로고    scopus 로고
    • 1-constrained quadratic programming (Lasso)
    • May
    • 1-constrained quadratic programming (Lasso). IEEE Trans. Information Theory, 55:2183-2202, May 2009.
    • (2009) IEEE Trans. Information Theory , vol.55 , pp. 2183-2202
    • Wainwright, M.J.1
  • 30
    • 3843104546 scopus 로고    scopus 로고
    • Nonparametric estimation of large covariance matrices of longitudinal data
    • W. B. Wu and M. Pourahmadi. Nonparametric estimation of large covariance matrices of longitudinal data. Biometrika, 90(4):831-844, 2003.
    • (2003) Biometrika , vol.90 , Issue.4 , pp. 831-844
    • Wu, W.B.1    Pourahmadi, M.2
  • 31
    • 33947115409 scopus 로고    scopus 로고
    • Model selection and estimation in the Gaussian graphical model
    • M. Yuan and Y. Lin. Model selection and estimation in the Gaussian graphical model. Biometrika, 94(1):19-35, 2007.
    • (2007) Biometrika , vol.94 , Issue.1 , pp. 19-35
    • Yuan, M.1    Lin, Y.2
  • 32


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.