267
Views
0
CrossRef citations to date
0
Altmetric
Original Articles

Estimation of a sparse and spiked covariance matrix

&
Pages 241-252 | Received 26 Mar 2014, Accepted 10 Feb 2015, Published online: 24 Mar 2015

References

  • Bertsekas, D.P. (2011), ‘Incremental proximal methods for large scale convex optimization’, Mathematical programming, 129, 163–195. doi: 10.1007/s10107-011-0472-0
  • Bickel, P.J., and Levina, E. (2008), ‘Covariance Regularization by Thresholding’, Annals of Statistics, 36, 2577–2604. doi: 10.1214/08-AOS600
  • Bickel, P.J., and Levina, E. (2008), ‘Regularized Estimation of Large Covariance Matrices’, The Annals of Statistics, 36, 199–227. doi: 10.1214/009053607000000758
  • Bien, J., and Tibshirani, R.J. (2011), ‘Sparse Estimation of a Covariance Matrix’, Biometrika, 98(4):807–820. doi: 10.1093/biomet/asr054
  • Cai, T., and Liu, W. (2011), ‘Adaptive Thresholding for Sparse Covariance Matrix Estimation’, Journal of the American Statistical Association, 106, 672–684. doi: 10.1198/jasa.2011.tm10560
  • Cai, T., Liu, W., and Luo, X. (2011), ‘A Constrained l1 Minimization Approach to Sparse Precision Matrix Estimation’, Journal of the American Statistical Association, 106(494):594–607. doi: 10.1198/jasa.2011.tm10155
  • Cai, T.T., Ma, Z., and Wu, Y. (2012), ‘Sparse PCA: Optimal Rates and Adaptive Estimation.’ arXiv preprint arXiv:1211.1309.
  • Cai, T., Ma, Z., and Wu, Y. (2013), ‘Optimal Estimation and Rank Detection for Sparse Spiked Covariance Matrices.’ arXiv preprint arXiv:1305.3235.
  • Cai, T.T., and Yuan, M. (2012), ‘Adaptive Covariance Matrix Estimation Through Block Thresholding’, The Annals of Statistics, 40(4):2014–2042. doi: 10.1214/12-AOS999
  • Cai, T.T., Zhang, C.-H., and Zhou, H.H. (2010), ‘Optimal Rates of Convergence for Covariance Matrix Estimation’, The Annals of Statistics, 38(4):2118–2144. doi: 10.1214/09-AOS752
  • Cai, T., and Zhou, H. (2012), ‘Minimax Estimation of Large Covariance Matrices Under l1 Norm (with discussion)’, Statistica Sinica, 22, 1319–1378.
  • Candès, E.J., Li, X., Ma, Y., and Wright, J. (2011), ‘Robust Principal Component Analysis?’, Journal of the ACM, 58(1):1–37. doi: 10.1145/1970392.1970395
  • Candès, E.J., and Recht, B. (2009), ‘Exact Matrix Completion via Convex Optimization’, Foundations of Computational Mathematics, 9(6):717–772. doi: 10.1007/s10208-009-9045-5
  • Fan, J.Q., Feng, Y., and Wu, Y. (2009), ‘Network Exploration via the Adaptive Lasso and SCAD Penalties’, Annals of Applied Statistics, 3(2):521–541. doi: 10.1214/08-AOAS215
  • Fan, J., Liao, Y., and Mincheva, M. (2011), ‘High-Dimensional Covariance Matrix Estimation in Approximate Factor Models’, Annals of Statistics, 39(6):3320–3356. doi: 10.1214/11-AOS944
  • Friedman, J., Hastie, T., and Tibshirani, R. (2008), ‘Sparse Inverse Covariance Estimation with the Graphical Lasso’, Biostatistics, 9(3):432–441. doi: 10.1093/biostatistics/kxm045
  • Koltchinskii, V., Lounici, K., and Tsybakov, A.B. (2011), ‘Nuclear-Norm Penalization and Optimal Rates for Noisy Low-Rank Matrix Completion’, The Annals of Statistics, 39(5):2302–2329. doi: 10.1214/11-AOS894
  • Lam, C., and Fan, J.Q. (2009), ‘Sparsistency and Rates of Convergence in Large Covariance Matrix Estimation’, Annals of Statistics, 37(6B):4254–4278. doi: 10.1214/09-AOS720
  • Lian, H. (2011), ‘Shrinkage Tuning Parameter Selection in Precision Matrices Estimation’, Journal of Statistical Planning and Inference, 141, 2839–2848. doi: 10.1016/j.jspi.2011.03.008
  • Negahban, S., and Wainwright, M.J. (2011), ‘Estimation of (near) Low-Rank Matrices with Noise and High-Dimensional Scaling’, The Annals of Statistics, 39(2):1069–1097. doi: 10.1214/10-AOS850
  • Peterson, L.E. (2002), ‘Factor Analysis of Cluster-Specific Gene Expression Levels from cDNA Microarrays’, Computer Methods and Programs in Biomedicine, 69(3):179–188. doi: 10.1016/S0169-2607(01)00189-4
  • Rothman, A.J. (2012), ‘Positive Definite Estimators of Large Covariance Matrices’, Biometrika, 99(3):733–740. doi: 10.1093/biomet/ass025
  • Rothman, A.J., Levina, E., and Zhu, J. (2009), ‘Generalized Thresholding of Large Covariance Matrices’, Journal of the American Statistical Association, 104(485):177–186. doi: 10.1198/jasa.2009.0101
  • Shapiro, A. (1985), ‘Identifiability of Factor Analysis: Some Results and Open Problems’, Linear Algebra and Its Applications, 70, 1–7. doi: 10.1016/0024-3795(85)90038-2
  • Tipping, M.E., and Bishop, C.M. (1999), ‘Probabilistic Principal Component Analysis’, Journal of the Royal Statistical Society: Series B (Statistical Methodology), 61(3):611–622. doi: 10.1111/1467-9868.00196
  • van't Veer, L.J. , Dai, H., van de Vijver, M.J., He, Y.D., Hart, A.A.M., Mao, M., Peterse, H.L., van der Kooy, K., Marton, M.J., Witteveen, A.T. , Schreiber, G.J., Kerkhoven, R.M., Roberts, C., Linsley, P.S., Bernards, R., and Friend, S.H. (2002), ‘Gene Expression Profiling Predicts Clinical Outcome of Breast Cancer’, Nature, 415(6871):530–536. doi: 10.1038/415530a
  • Wen, Z., Yin, W., and Zhang, Y. (2012), ‘Solving a Low-Rank Factorization Model for Matrix Completion by a Nonlinear Successive Over-Relaxation Algorithm’, Mathematical Programming Computation, 4(4):333–361. doi: 10.1007/s12532-012-0044-1
  • Wu, W.B., and Pourahmadi, M. (2003), ‘Nonparametric Estimation of Large Covariance Matrices of Longitudinal Data’, Biometrika, 90(4):831–844. doi: 10.1093/biomet/90.4.831
  • Xue, L., Ma, S., and Zou, H. (2012), ‘Positive-Definite l1-Penalized Estimation of Large Covariance Matrices’, Journal of the American Statistical Association, 107(500):1480–1491. doi: 10.1080/01621459.2012.725386
  • Zou, H., Hastie, T., and Tibshirani, R. (2006), ‘Sparse Principal Component Analysis’, Journal of Computational and Graphical Statistics, 15(2):265–286. doi: 10.1198/106186006X113430

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.