526
Views
2
CrossRef citations to date
0
Altmetric
Theory and Methods

Minimax and Adaptive Estimation of Covariance Operator for Random Variables Observed on a Lattice Graph

Pages 253-265 | Received 01 Oct 2010, Published online: 05 May 2016

REFERENCES

  • Bickel, P. Levina, E. (2008a), Regularized Estimation of Large Covariance Matrices, The Annals of Statistics, 36, 199–227.
  • ——— (2008b), Covariance Regularization by Thresholding, The Annals of Statistics, 36, 2577–2604.
  • Cai, T.T., Liu, W. (2011), Adaptive Thresholding for Sparse Covariance Matrix Estimation, Journal of the American Statistical Association, 494, 672–684.
  • Cai, T.T., Liu, W., Luo, X. (2011), A Constrained ℓ1 Minimization Approach to Sparse Precision Matrix Estimation, Journal of the American Statistical Association, 494, 594–607.
  • Cai, T.T., Liu, W., Zhou, H.H. (2011), Optimal Estimation of Large Sparse Precision Matrices, unpublished manuscript.
  • Cai, T.T., Yuan, M. (2012), Adaptive Covariance Matrix Estimation Through Block Thresholding, The Annals of Statistics, 40, 2014–2042.
  • Cai, T.T., Zhang, C.H., Zhou, H. (2010), Optimal Rates of Convergence for Covariance Matrix Estimation, The Annals of Statistics, 38, 2118–2144.
  • Cai, T.T. Zhou, H. (2012), Optimal Rates of Convergence for Sparse Covariance Matrix Estimation, The Annals of Statistics, 40, 2389–2420.
  • El Karoui, N. (2008), Operator Norm Consistent Estimation of Large Dimensional Sparse Covariance Matrices, The Annals of Statistics, 36, 2717–2756.
  • Fan, J., Fan, Y., Lv, J. (2008), High Dimensional Covariance Matrix Estimation Using a Factor Model Journal of Econometrics, 147, 186–197.
  • Friedman, J., Hastie, T., Tibshirani, T. (2008), Sparse Inverse Covariance Estimation With the Graphical Lasso, Biostatistics, 9, 432–441.
  • Huang, J., Liu, N., Pourahmadi, M., Liu, L. (2006), Covariance Matrix Selection and Estimation via Penalised Normal Likelihood, Biometrika, 93, 85–98.
  • Johnstone, I., Lu, A. (2009), On Consistency and Sparsity for Principal Components Analysis in High Dimensions, Journal of the American Statistical Association, 104, 682–693.
  • Krause, E. (1987), Taxicab Geometry. New York: Dover.
  • Lam, C. Fan, J. (2009), Sparsistency and Rates of Convergence in Large Covariance Matrix Estimation, The Annals of Statistics, 37, 4254–4278.
  • Ledoit, O. Wolf, M. (2004), A Well-Conditioned Estimator for Large-dimensional Covariance Matrices, Journal of Multivariate Analysis, 88, 365–411.
  • Rothman, A., Bickel, P., Levina, E., Zhu, J. (2008), Sparse Permutation Invariant Covariance Estimation, Electronic Journal of Statistics, 2, 494–515.
  • Rothman, A., Levina, E., Zhu, J. (2009), Generalized Thresholding of Large Covariance Matrices, Journal of the American Statistical Association, 104, 177–186.
  • Rudelson, M. (1999), Random Vectors in the Isotropic Position,, Journal of Functional Analysis, 164, 60–72.
  • Samaria, F., Harter, A. (1994), Parameterisation of a Stochastic Model for Human Face Identification, in Proceedings of 2nd IEEE Workshop on Applications of Computer Vision, Sarasota, FL, pp. 138–142.
  • Sirovich, L., Kirby, M. (1987), Low-Dimensional Procedure for the Characterization of Human Faces, Journal of the Optical Society of America A, 4, 519–524.
  • Tsybakov, A. (2009), Introduction to Nonparametric Estimation, New York: Springer.
  • Turk, M., Pentland, A. (1991), Eigenfaces for Recognition, Journal of Cognitive Neuroscience, 3, 71–86.
  • Yuan, M. (2010), Sparse Inverse Covariance Matrix Estimation Via Linear Programming, Journal of Machine Learning Research, 11, 2261–2286.
  • Yuan, M., Lin, Y. (2007), Model Selection and Estimation in the Gaussian Graphical Model, Biometrika, 94, 19–35.

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.