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Original Articles

Sparse Covariance Matrix Estimation With Eigenvalue Constraints

Pages 439-459 | Received 01 Jul 2012, Published online: 28 Apr 2014

REFERENCES

  • Bickel, P., and Levina, E. (2004), “Some Theory for Fisher’s Linear Discriminant Function, ‘Naive Bayes,’ and Some Alternatives When There are Many More Variables Than Observations,” Bernoulli, 10, 989–1010.
  • Bickel, P., and Levina, E. (2008a), “Covariance Regularization by Thresholding,” The Annals of Statistics, 36, 2577–2604.
  • Bickel, P., and Levina, E. (2008b), “Regularized Estimation of Large Covariance Matrices,” The Annals of Statistics, 36, 199–227.
  • Bien, J., and Tibshirani, R. (2011), “Sparse Estimation of a Covariance Matrix,” Biometrika, 98, 807–820.
  • Box, G., Jenkins, G., and Reinsel, G. (1994), Time Series Analysis (3rd ed.), Prentice Hall.
  • Cai, T., and Liu, W. (2011), “Adaptive Thresholding for Sparse Covariance Matrix Estimation,” Journal of the American Statistical Association, 106, 672–684.
  • Cai, T., Zhang, C., and Zhou, H. (2010), “Optimal Rates of Convergence for Covariance Matrix Estimation,” The Annals of Statistics, 38, 2118–2144.
  • Cai, T., and Zhou, H. (2012), “Optimal Rates of Convergence for Sparse Covariance Matrix Estimation,” The Annals of Statistics, 40, 2389–2420.
  • Chen, S., Donoho, D., and Saunders, M. (1998), “Atomic Decomposition by Basis Pursuit,” SIAM Journal on Scientific Computing, 20, 33–61.
  • Cressie, N. (1992), “Statistics for Spatial Data,” Terra Nova, 4, 613–617.
  • Fan, J., and Li, R. (2001), “Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties,” Journal of the American Statistical Association, 96, 1348–1360.
  • Furrer, R., and Bengtsson, T. (2007), “Estimation of High-Dimensional Prior and Posterior Covariance Matrices in Kalman Filter Variants,” Journal of Multivariate Analysis, 98, 227–255.
  • Gabay, D., and Mercier, B. (1976), “A Dual Algorithm for the Solution of Nonlinear Variational Problems via Finite Element Approximation,” Computers & Mathematics with Applications, 2, 17–40.
  • Han, F., and Liu, H. (2012), “Semiparametric Principal Component Analysis,” Advances in Neural Information Processing Systems, 171–179.
  • Han, F., Zhao, T., and Liu, H. (2013), “Coda: High Dimensional Copula Discriminant Analysis,” Journal of Machine Learning Research, 14, 629–671.
  • He, B., and Yuan, X. (2012), “On Non-Ergodic Convergence Rate of Douglas-Rachford Alternating Direction Method of Multipliers,” Technical Report, Nanjing University.
  • Huang, J., Liu, N., Pourahmadi, M., and Liu, L. (2006), “Covariance Matrix Selection and Estimation via Penalised Normal Likelihood,” Biometrika, 93, 85–98.
  • Karoui, N. (2008), “Operator Norm Consistent Estimation of Large Dimensional Sparse Covariance Matrices,” The Annals of Statistics, 36, 2717–2756.
  • Lam, C., and Fan, J. (2009), “Sparsistency and Rates of Convergence in Large Covariance Matrix Estimation,” The Annals of Statistics, 37, 42–54.
  • Levina, E., Rothman, A., and Zhu, J. (2008), “Sparse Estimation of Large Covariance Matrices via a Nested Lasso Penalty,” The Annals of Applied Statistics, 2, 245–263.
  • Liu, H., Han, F., Yuan, M., Lafferty, J., and Wasserman, L. (2012), “High Dimensional Semiparametric Gaussian Copula Graphical Models,” The Annals of Statistics, 40, 2293–2326.
  • Liu, H., Lafferty, J., and Wasserman, L. (2009), “The Nonparanormal: Semiparametric Estimation of High Dimensional Undirected Graphs,” Journal of Machine Learning Research, 10, 2295–2328.
  • Negahban, S., Ravikumar, P., Wainwright, M., and Yu, B. (2012), “A Unified Framework for High-Dimensional Analysis of m-Estimators With Decomposable Regularizers,” Statistical Science, 27, 538–557.
  • Rothman, A. (2012), “Positive Definite Estimators of Large Covariance Matrices,” Biometrika, 99, 733–740.
  • Rothman, A., Bickel, P., Levina, E., and Zhu, J. (2008), “Sparse Permutation Invariant Covariance Estimation,” Electronic Journal of Statistics, 2, 494–515.
  • Rothman, A., Levina, E., and Zhu, J. (2009), “Generalized Thresholding of Large Covariance Matrices,” Journal of the American Statistical Association, 104, 177–186.
  • Rothman, A., Levina, E., and Zhu, J. (2010), “A New Approach to Cholesky-based Covariance Regularization in High Dimensions,” Biometrika, 97, 539–550.
  • Searle, S., Casella, G., and McCulloch, C. (1992), Variance Components (Vol. 419), Wiley Online Library.
  • Tibshirani, R. (1996), “Regression Shrinkage and Selection via the Lasso,” Journal of the Royal Statistical Society, Series B, 58, 267–288.
  • Wu, W., and Pourahmadi, M. (2003), “Nonparametric Estimation of Large Covariance Matrices of Longitudinal Data,” Biometrika, 90, 831–844.
  • Xue, L., Ma, S., and Zou, H. (2012), “Positive Definite l1 Penalized Estimation of Large Covariance Matrices,” Journal of the American Statistical Association, 107, 1480–1491.
  • Xue, L., and Zou, H. (2012), “Regularized Rank-Based Estimation of High-Dimensional Nonparanormal Graphical Models,” The Annals of Statistics, 40, 2541–2571.
  • Zhang, C. (2010), “Nearly Unbiased Variable Selection Under Minimax Concave Penalty,” The Annals of Statistics, 38, 894–942.
  • Zou, H. (2006), “The Adaptive Lasso and its Oracle Properties,” Journal of the American Statistical Association, 101, 1418–1429.

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