An improved modified cholesky decomposition approach for precision matrix estimation

References

• Meinshausen N, Bhlmann P. High-dimensional graphs and variable selection with the lasso. Ann Statist. 2006;34(3):1436–1462. doi: 10.1214/009053606000000281
   Web of Science ®Google Scholar
• Yuan M, Lin Y. Model selection and estimation in the Gaussian graphical model. Biometrika. 2007;94(1):19–35. doi: 10.1093/biomet/asm018
   Web of Science ®Google Scholar
• Friedman J, Hastie T, Tibshirani R. Sparse inverse covariance estimation with the graphical lasso. Biostatistics. 2008;9(3):432–441. doi: 10.1093/biostatistics/kxm045
   PubMed Web of Science ®Google Scholar
• Rocha GV, Zhao P, Yu B. A path following algorithm for sparse pseudo-likelihood inverse covariance estimation (splice). Preprint, 2008. arXiv:0807.3734.
   Google Scholar
• Rothman AJ, Bickel PJ, Levina E, et al. Sparse permutation invariant covariance estimation. Electron J Stat. 2008;2:494–515. doi: 10.1214/08-EJS176
   Web of Science ®Google Scholar
• Yuan M. Efficient computation of ℓ1 regularized estimates in Gaussian graphical models. J Comput Graph Stat. 2008;17(4):809–826. doi: 10.1198/106186008X382692
   Web of Science ®Google Scholar
• Deng X, Yuan M. Large Gaussian covariance matrix estimation with Markov structures. J Comput Graph Stat. 2009;18(3):640–657. doi: 10.1198/jcgs.2009.07170
   Web of Science ®Google Scholar
• Yuan M. High dimensional inverse covariance matrix estimation via linear programming. J Mach Learn Res. 2010;11:2261–2286.
   Web of Science ®Google Scholar
• Raskutti G, Yu B, Wainwright MJ, et al. Model Selection in Gaussian Graphical Models: High-Dimensional Consistency of ℓ1-regularized MLE. In Advances in Neural Information Processing Systems. 2009; p. 1329–1336.
   Google Scholar
• Lam C, Fan J. Sparsistency and rates of convergence in large covariance matrix estimation. Ann Stat. 2009;37(6):4254–4278. doi: 10.1214/09-AOS720
   PubMed Web of Science ®Google Scholar
• Fan J, Fan Y, Lv J. High dimensional covariance matrix estimation using a factor model. J Econom. 2008;147(1):186–197. doi: 10.1016/j.jeconom.2008.09.017
   Web of Science ®Google Scholar
• Xue L, Zou H. Regularized rank-based estimation of high-dimensional nonparanormal graphical models. Ann Statist. 2012;40(5):2541–2571. doi: 10.1214/12-AOS1041
   Web of Science ®Google Scholar
• Wieringen WN, Peeters CF. Ridge estimation of inverse covariance matrices from high-dimensional data. Comput Stat Data Anal. 2016;103:284–303. doi: 10.1016/j.csda.2016.05.012
   Web of Science ®Google Scholar
• Drton M, Perlman MD. A SINful approach to Gaussian graphical model selection. J Stat Plan Inference. 2008;138(4):1179–1200. doi: 10.1016/j.jspi.2007.05.035
   Web of Science ®Google Scholar
• Sun T, Zhang C. Comment: minimax estimation of large covariance matrices under ℓ-1 norm. Statist Sinica. 2012;22:1354–1358. doi: 10.5705/ss.2010.093
   Web of Science ®Google Scholar
• Cheng Y, Lenkoski A. Hierarchical Gaussian graphical models: beyond reversible jump. Electron J Stat. 2012;6:2309–2331. doi: 10.1214/12-EJS746
   Web of Science ®Google Scholar
• Wang H. Bayesian graphical lasso models and efficient posterior computation. Bayesian Anal. 2012;7(4):867–886. doi: 10.1214/12-BA729
   Web of Science ®Google Scholar
• Bhadra A, Mallick BK. Joint high-dimensional Bayesian variable and covariance selection with an application to eQTL analysis. Biometrics. 2013;69(2):447–457. doi: 10.1111/biom.12021
   PubMed Web of Science ®Google Scholar
• Scutari M. On the prior and posterior distributions used in graphical modelling. Bayesian Anal. 2013;8(3):505–532. doi: 10.1214/13-BA819
   Web of Science ®Google Scholar
• Mohammadi A, Wit EC. Bayesian structure learning in sparse Gaussian graphical models. Bayesian Anal. 2015;10(1):109–138. doi: 10.1214/14-BA889
   Web of Science ®Google Scholar
• Pourahmadi M. Joint mean-covariance models with applications to longitudinal data: unconstrained parameterisation. Biometrika. 1999;86(3):677–690. doi: 10.1093/biomet/86.3.677
   Web of Science ®Google Scholar
• Pourahmadi M. Foundations of time series analysis and prediction theory. New York: John Wiley & Sons; 2001.
   Google Scholar
• Chang C, Tsay RS. Estimation of covariance matrix via the sparse Cholesky factor with lasso. J Stat Plan Inference. 2010;140(12):3858–3873. doi: 10.1016/j.jspi.2010.04.048
   Web of Science ®Google Scholar
• Chen Z, Leng C. Local linear estimation of covariance matrices via Cholesky decomposition. Stat Sin. 2015;25(3):1249–1263.
   Web of Science ®Google Scholar
• Zheng H, Tsui KW, Kang X, et al. Cholesky-based model averaging for covariance matrix estimation. Statist Theory Related Fields. 2017;1(1):48–58. doi: 10.1080/24754269.2017.1336831
   Google Scholar
• Wagaman AS, Levina E. Discovering sparse covariance structures with the isomap. J Comput Graph Stat. 2009;18(3):551–572. doi: 10.1198/jcgs.2009.08021
   Web of Science ®Google Scholar
• Rajaratnam B, Salzman J. Best permutation analysis. J Multivar Anal. 2013;121:193–223. doi: 10.1016/j.jmva.2013.03.001
   Web of Science ®Google Scholar
• Tibshirani R. Regression shrinkage and selection via the lasso. J R Statist Soc Ser B (Methodological). 1996;58:267–288.
   Web of Science ®Google Scholar
• Huang JZ, Liu N, Pourahmadi M, et al. Covariance matrix selection and estimation via penalised normal likelihood. Biometrika. 2006;93(1):85–98. doi: 10.1093/biomet/93.1.85
   Web of Science ®Google Scholar
• Kang X, Xie C, Wang M. A Cholesky-based estimation for large-dimensional covariance matrices. J Appl Stat. 2019. in press. doi:10.1080/02664763.2019.1664424.
   Web of Science ®Google Scholar
• Guo J, Levina E, Michailidis G, et al. Joint estimation of multiple graphical models. Biometrika. 2011;98(1):1–15. doi: 10.1093/biomet/asq060
   PubMed Web of Science ®Google Scholar
• Dellaportas P, Pourahmadi M. Cholesky-GARCH models with applications to finance. Stat Comput. 2012;22(4):849–855. doi: 10.1007/s11222-011-9251-2
   Web of Science ®Google Scholar
• Bickel PJ, Levina E. Some theory for fisher's linear discriminant function,naive bayes', and some alternatives when there are many more variables than observations. Bernoulli. 2004;10(6):989–1010. doi: 10.3150/bj/1106314847
   Web of Science ®Google Scholar
• Friedman JH. Regularized discriminant analysis. J Am Stat Assoc. 1989;84(405):165–175. doi: 10.1080/01621459.1989.10478752
   Web of Science ®Google Scholar
• Howland P, Park H. Generalizing discriminant analysis using the generalized singular value decomposition. IEEE Trans Pattern Anal Mach Intell. 2004;26(8):995–1006. doi: 10.1109/TPAMI.2004.46
   PubMed Web of Science ®Google Scholar
• Guo Y, Hastie T, Tibshirani R. Regularized linear discriminant analysis and its application in microarrays. Biostatistics. 2006;8(1):86–100. doi: 10.1093/biostatistics/kxj035
   PubMed Web of Science ®Google Scholar
• Fan J, Fan Y. High dimensional classification using features annealed independence rules. Ann Stat. 2008;36(6):2605–2637. doi: 10.1214/07-AOS504
   PubMed Web of Science ®Google Scholar
• Shao J, Wang Y, Deng X, et al. Sparse linear discriminant analysis by thresholding for high dimensional data. Ann Statist. 2011;39(2):1241–1265. doi: 10.1214/10-AOS870
   Web of Science ®Google Scholar
• Quinlan RC. 4.5: Programs for machine learning morgan. San Francisco, USA: Kaufmann Publishers Inc; 1993.
   Google Scholar
• Dudoit S, Fridlyand J, Speed TP. Comparison of discrimination methods for the classification of tumors using gene expression data. J Am Stat Assoc. 2002;97(457):77–87. doi: 10.1198/016214502753479248
   Web of Science ®Google Scholar
• Jiang X. Joint estimation of covariance matrix via Cholesky Decomposition [Doctoral dissertation]. 2012.
   Google Scholar