메뉴 건너뛰기




Volumn 40, Issue 2, 2012, Pages 1024-1060

Nonlinear shrinkage estimation of large-dimensional covariance matrices

Author keywords

Large dimensional asymptotics; Nonlinear shrinkage; Rotation equivariance

Indexed keywords


EID: 84872012313     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/12-AOS989     Document Type: Article
Times cited : (465)

References (24)
  • 1
    • 22044453079 scopus 로고    scopus 로고
    • No eigenvalues outside the support of the limiting spectral distribution of large-dimensional sample covariance matrices
    • Mr1617051
    • Bai, Z. D. and Silverstein, J. W. (1998). No Eigenvalues Outside The Support of The Limiting Spectral Distribution of Large-Dimensional Sample Covariance Matrices. Ann. Probab. 26 316-345. Mr1617051
    • (1998) Ann. Probab. , vol.26 , pp. 316-345
    • Bai, Z.D.1    Silverstein, J.W.2
  • 2
    • 41549106844 scopus 로고    scopus 로고
    • Regularized estimation of large covariance matrices
    • Mr2387969
    • Bickel, P. J. and Levina, E. (2008). Regularized Estimation of Large Covariance Matrices. Ann. Statist. 36 199-227. Mr2387969
    • (2008) Ann. Statist. , vol.36 , pp. 199-227
    • Bickel, P.J.1    Levina, E.2
  • 3
    • 84861177056 scopus 로고    scopus 로고
    • Minimax estimation of large covariance matrices under 1 norm
    • to Appear
    • Cai, T. and Zhou, H. (2012). Minimax Estimation of Large Covariance Matrices Under 1 Norm. Statist. Sinica. to Appear.
    • (2012) Statist. Sinica.
    • Cai, T.1    Zhou, H.2
  • 4
    • 62349116164 scopus 로고    scopus 로고
    • Spectrum estimation for large dimensional covariance matrices using random matrix theory
    • Mr2485012
    • El Karoui, N. (2008). Spectrum Estimation for Large Dimensional Covariance Matrices Using Random Matrix Theory. Ann. Statist. 36 2757-2790. Mr2485012
    • (2008) Ann. Statist. , vol.36 , pp. 2757-2790
    • El Karoui, N.1
  • 5
    • 55349144848 scopus 로고    scopus 로고
    • High dimensional covariance matrix estimation using a factor model
    • Mr2472991
    • Fan, J., Fan, Y. and Lv, J. (2008). High Dimensional Covariance Matrix Estimation Using A Factor Model. J. Econometrics 147 186-197. Mr2472991
    • (2008) J. Econometrics , vol.147 , pp. 186-197
    • Fan, J.1    Fan, Y.2    Lv, J.3
  • 6
    • 0036433588 scopus 로고    scopus 로고
    • Snopt: An sqp algorithm for largescale constrained optimization
    • (Electronic). Mr1922505
    • Gill, P. E., Murray, W. and Saunders, M. A. (2002). Snopt: An Sqp Algorithm for Largescale Constrained Optimization. Siam J. Optim. 12 979-1006 (Electronic). Mr1922505
    • (2002) Siam J. Optim. , vol.12 , pp. 979-1006
    • Gill, P.E.1    Murray, W.2    Saunders, M.A.3
  • 7
    • 0000406169 scopus 로고
    • Empirical bayes estimation of the multivariate normal covariance matrix
    • Mr0568722
    • Haff, L. R. (1980). Empirical Bayes Estimation of The Multivariate Normal Covariance Matrix. Ann. Statist. 8 586-597. Mr0568722
    • (1980) Ann. Statist. , vol.8 , pp. 586-597
    • Haff, L.R.1
  • 8
    • 0001486499 scopus 로고
    • Estimation with quadratic loss
    • Univ. California Press, Berkeley, Calif. Mr0133191
    • James, W. and Stein, C. (1961). Estimation with Quadratic Loss. in Proc. 4Th Berkeley Sympos. Math. Statist. and Prob., Vol. I 361-379. Univ. California Press, Berkeley, Calif. Mr0133191
    • (1961) Proc. 4Th Berkeley Sympos. Math. Statist. and Prob. , vol.1 , pp. 361-379
    • James, W.1    Stein, C.2
  • 9
    • 82255187067 scopus 로고    scopus 로고
    • Wishart distributions for decomposable covariance graph models
    • Mr2797855
    • Khare, K. and Rajaratnam, B. (2011).Wishart Distributions for Decomposable Covariance Graph Models. Ann. Statist. 39 514-555. Mr2797855
    • (2011) Ann. Statist. , Issue.39 , pp. 514-555
    • Khare, K.1    Rajaratnam, B.2
  • 10
    • 80052806822 scopus 로고    scopus 로고
    • Eigenvectors of some large sample covariance matrix ensembles
    • Mr2834718
    • Ledoit, O. and Péché, S. (2011). Eigenvectors of Some Large Sample Covariance Matrix Ensembles. Probab. Theory Related Fields 151 233-264. Mr2834718
    • (2011) Probab. Theory Related Fields , vol.151 , pp. 233-264
    • Ledoit, O.1    Péché, S.2
  • 11
    • 0346961488 scopus 로고    scopus 로고
    • A well-conditioned estimator for large-dimensional covariance matrices
    • Mr2026339
    • Ledoit, O. andwolf, M. (2004). A Well-Conditioned Estimator for Large-Dimensional Covariance Matrices. J. Multivariate Anal. 88 365-411. Mr2026339
    • (2004) J. Multivariate Anal. , Issue.88 , pp. 365-411
    • Ledoit, O.1    Wolf, M.2
  • 13
    • 0000263234 scopus 로고
    • Distribution of eigenvalues for some sets of random matrices
    • Marc Enko, V. A. and Pastur, L. A. (1967). Distribution of Eigenvalues for Some Sets of Random Matrices. Sbornik: Mathematics 1 457-483.
    • (1967) Sbornik: Mathematics 1 , pp. 457-483
    • Marcenko, V.1    Pastur, L.2
  • 14
    • 30344437591 scopus 로고    scopus 로고
    • Finite sample size effect on minimum variance beamformers: Optimum diagonal loading factor for large arrays
    • Mestre, X. and Lagunas, M. A. (2006). Finite Sample Size Effect on Minimum Variance Beamformers: Optimum Diagonal Loading Factor for Large Arrays. Ieee Trans. Signal Process. 54 69-82.
    • (2006) Ieee Trans. Signal Process. , vol.54 , pp. 69-82
    • Mestre, X.1    Lagunas, M.A.2
  • 16
    • 62349133125 scopus 로고    scopus 로고
    • Flexible covariance estimation in graphical gaussian models
    • Mr2485014
    • Rajaratnam, B.,Massam, H. and Carvalho, C. M. (2008). Flexible Covariance Estimation in Graphical Gaussian Models. Ann. Statist. 36 2818-2849. Mr2485014
    • (2008) Ann. Statist. , Issue.36 , pp. 2818-2849
    • Rajaratnam, B.1    Massam, H.2    Carvalho, C.M.3
  • 18
    • 79952902758 scopus 로고    scopus 로고
    • Estimation of high-dimensional low-rank matrices
    • Mr2816342
    • Rohde, A. and Tsybakov, A. B. (2011). Estimation of High-Dimensional Low-Rank Matrices. Ann. Statist. 39 887-930. Mr2816342
    • (2011) Ann. Statist. , Issue.39 , pp. 887-930
    • Rohde, A.1    Tsybakov, A.B.2
  • 20
    • 0002627253 scopus 로고
    • Strong convergence of the empirical distribution of eigenvalues of largedimensional random matrices
    • Mr1370408
    • Silverstein, J. W. (1995). Strong Convergence of The Empirical Distribution of Eigenvalues of Largedimensional Random Matrices. J. Multivariate Anal. 55 331-339. Mr1370408
    • (1995) J. Multivariate Anal. , vol.55 , pp. 331-339
    • Silverstein, J.W.1
  • 21
    • 58149320175 scopus 로고
    • Analysis of the limiting spectral distribution of largedimensional random matrices
    • Mr1345541
    • Silverstein, J.W. and Choi, S.-I. (1995). Analysis of The Limiting Spectral Distribution of Largedimensional Random Matrices. J. Multivariate Anal. 54 295-309. Mr1345541
    • (1995) J. Multivariate Anal. , vol.54 , pp. 295-309
    • Silverstein, J.W.1    Choi, S.-I.2
  • 22
    • 0000813561 scopus 로고
    • Inadmissibility of the usual estimator for the mean of a multivariate normal distribution
    • Univ. California Press, Berkeley. Mr0084922
    • Stein, C. (1956). inadmissibility of The Usual Estimator for The Mean of A Multivariate Normal Distribution. in Proceedings of The Third Berkeley Symposium on Mathematical Statistics and Probability, 1954-1955, Vol. I 197-206. Univ. California Press, Berkeley. Mr0084922
    • (1956) Proceedings of The Third Berkeley Symposium on Mathematical Statistics and Probability, 1954-1955 , vol.1 , pp. 197-206
    • Stein, C.1
  • 23
    • 34249722106 scopus 로고
    • Estimation of a covariance matrix. Rietz lecture
    • Atlanta, Georgia
    • Stein, C. (1975). Estimation of A Covariance Matrix. Rietz Lecture, 39Th Annual Meeting Ims. Atlanta, Georgia.
    • (1975) 39Th Annual Meeting Ims
    • Stein, C.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.