References
- Bickel, P. J., and E. Levina. 2008a. Regularized estimation of large covariance matrices. The Annals of Statistics 36 (1):199–227. doi:10.1214/009053607000000758.
- Bickel, P. J., and E. Levina. 2008b. Covariance regularization by thresholding. The Annals of Statistics 36 (6):2577–604. doi:10.1214/08-AOS600.
- Bien, J., and R. J. Tibshirani. 2011. Sparse estimation of a covariance matrix. Biometrika 98 (4):807–20. doi:10.1093/biomet/asr054.
- Borg, I., and P. Groenen. 2005. Modern multidimensional scaling: Theory and applications. New York: Springer Press.
- Chang, C., and R. Tsay. 2010. Estimation of covariance matrix via the sparse Cholesky factor with Lasso. Journal of Statistical Planning and Inference 140 (12):3858–73. doi:10.1016/j.jspi.2010.04.048.
- Dellaportas, P., and M. Pourahmadi. 2012. Cholesky-GARCH models with applications to finance. Statistics and Computing 22 (4):849–55. doi:10.1007/s11222-011-9251-2.
- Fan, J., and Y. Fan. 2008. High dimensional classification using features annealed independence rules. Annals of Statistics 36 (6):2605–37. doi:10.1214/07-AOS504.
- Guo, J., E. Levina, G. Michailidis, and J. Zhu. 2011. Joint estimation of multiple graphical models. Biometrika 98 (1):1–15. doi:10.1093/biomet/asq060.
- Huang, J. Z., N. Liu, M. Pourahmadi, and L. Liu. 2006. Covariance matrix selection and estimation via penalised normal likelihood. Biometrika 93 (1):85–98. doi:10.1093/biomet/93.1.85.
- Jiang, X. 2012. Joint estimation of multiple graphical models. PhD diss., Department of Statistics and Applied Probability, National University of Singapore.
- Kang, X., and X. Deng. 2020. An improved modified Cholesky decomposition approach for precision matrix estimation. Journal of Statistical Computation and Simulation 90 (3):443–64. doi:10.1080/00949655.2019.1687701.
- Kang, X., X. Deng, K. Tsui, and M. Pourahmadi. 2020. On variable ordination of modified Cholesky decomposition for estimating time-varying covariance matrices. International Statistical Review 88 (3):616–41. doi:10.1111/insr.12357.
- Kang, X., and M. Wang. 2021. Ensemble sparse estimation of covariance matrix for exploring genetic disease data. Computational Statistics and Data Analysis 159 :107220. doi:10.1016/j.csda.2021.107220.
- Kang, X., C. Xie, and M. Wang. 2020. A Cholesky-based estimation for large-dimensional covariance matrices. Journal of Applied Statistics 47 (6):1017–30. doi:10.1080/02664763.2019.1664424.
- Lam, C., and J. Fan. 2009. Sparsistency and rates of convergence in large covariance matrix estimation. Annals of Statistics 37 (6B):4254–78. doi:10.1214/09-AOS720.
- Rajaratnam, B., and J. Salzman. 2013. Best permutation analysis. Journal of Multivariate Analysis 121:193–223. doi:10.1016/j.jmva.2013.03.001.
- Rothman, A., P. Bickel, E. Levina, and J. Zhu. 2008. Sparse permutation invariant covariance estimation. Electronic Journal of Statistics 2 (none):494–515. doi:10.1214/08-EJS176.
- Rothman, A. J., E. Levina, and J. Zhu. 2009. Generalized thresholding of large covariance matrices. Journal of the American Statistical Association 104 (485):177–86. doi:10.1198/jasa.2009.0101.
- Rothman, A. J., E. Levina, and J. Zhu. 2010. A new approach to Cholesky-based covariance regularization in high dimensions. Biometrika 97 (3):539–50. doi:10.1093/biomet/asq022.
- Tenenbaum, J. B., V. de Silva, and J. C. Langford. 2000. A global geometric framework for nonlinear dimensionality reduction. Science (New York, N.Y.) 290 (5500):2319–23. doi:10.1126/science.290.5500.2319.
- Tibshirani, R. 1996. Regression shrinkage and selection via the Lasso. Journal of the Royal Statistical Society: Series B (Methodological) 58 (1):267–88. doi:10.1111/j.2517-6161.1996.tb02080.x.
- Wagaman, A. S., and E. Levina. 2009. Discovering sparse covariance structures with the Isomap. Journal of Computational and Graphical Statistics 18 (3):551–72. doi:10.1198/jcgs.2009.08021.
- Wegkamp, M., and Y. Zhao. 2016. Adaptive estimation of the copula correlation matrix for semiparametric elliptical copulas. Bernoulli 22 (2):1184–226. doi:10.3150/14-BEJ690.
- Won, J. H., J. Lim, S. J. Kim, and B. Rajaratnam. 2013. Condition number regularized covariance estimation. Journal of the Royal Statistical Society. Series B, Statistical Methodology 75 (3):427–50. doi:10.1111/j.1467-9868.2012.01049.x.
- Xue, L., S. Ma, and H. Zou. 2012. Positive-definite L1-penalized estimation of large covariance matrices. Journal of the American Statistical Association 107 (500):1480–91. doi:10.1080/01621459.2012.725386.
- Zhao, T., K. Roeder, and H. Liu. 2014. Positive semidefinite rank-based correlation matrix estimation with application to semiparametric graph estimation. Journal of Computational and Graphical Statistics: A Joint Publication of American Statistical Association, Institute of Mathematical Statistics, Interface Foundation of North America 23 (4):895–922. doi:10.1080/10618600.2013.858633.
- Zheng, H., K. Tsui, X. Kang, and X. Deng. 2017. Cholesky-based model averaging for covariance matrix estimation. Statistical Theory and Related Fields 1 (1):48–58. doi:10.1080/24754269.2017.1336831.