[1] |
SCHFER J, STRIMMER K. A shrinkage approach to large-scale covariance matrix estimation and implications for functional genomics[J]. Statistical Applications in Genetics and Molecular Biology, 2005, 4(1): Article 32.
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[2] |
CHEN X, LIU Y, LIU H, et al. Learning spatial-temporal varying graphs with applications to climate data analysis[C]// Proceedings of the Twenty-Fourth AAAI Conference on Artificial Intelligence. Palo Alto, CA: Association for the Advancement of Artificial Intelligence, 2010: 425-430.
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[3] |
FAN J, LIAO Y, LIU H. An overview of the estimation of large covariance and precision matrices [J]. Econometrics Journal, 2016, 19(1): C1-C32.
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[4] |
WAINWRIGHT M J, JORDAN M I. Graphical Models, Exponential Families, and Variational Inference [M]. Hanover,MA: Now, 2008.
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[5] |
LIU H, LAFFERTY J, WASSERMAN L. The nonparanormal: Semiparametric estimation of high dimensional undirected graphs [J]. Journal of Machine Learning Research, 2009, 10(3): 2295-2328.
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[6] |
LAURITZEN S. Graphical Models [M]. New York: Oxford Univ Press, 1996.
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[7] |
MEINSHAUSEN N, BHLMANN P. High-dimensional graphs and variable selection with the Lasso [J]. The Annals of Statistics, 2006, 34(3): 1436-1462.
|
[8] |
BICKEL P J, LEVINA E. Covariance regularization by thresholding[J]. The Annals of Statistics, 2008, 36(6): 2577-2604.
|
[9] |
RAVIKUMAR P, WAINWRIGHT M J, RASKUTTI G, et al. High-dimensional covariance estimation by minimizing 1-penalized log-determinant divergence[J]. Electronic Journal of Statistics, 2011, 5: 935-980.
|
[10] |
LIU W, LUO X. Fast and adaptive sparse precision matrix estimation in high dimensions[J]. Journal of Multivariate Analysis, 2015, 135:153-162.
|
[11] |
REN Z, SUN T, ZHANG C, et al. Asymptotic normality and optimalities in estimation of large Gaussian graphical models[J]. The Annals of Statistics, 2015, 43(3): 991-1026.
|
[12] |
FAN Y, LV J. Innovated scalable efficient estimation in ultra-large Gaussian graphical models[J]. The Annals of Statistics, 2016, 44(5): 2098-2126.
|
[13] |
CAI T, LIU W, LUO X. A constrained 1 minimization approach to sparse precision matrix estimation[J]. Journal of the American Statistical Association, 2011, 106: 594-607.
|
[14] |
NICKL R,VAN DE GEER S. Confidence sets in sparse regression[J]. The Annals of Statistics, 2013, 41(6): 2852-2876.
|
[15] |
VAN DE GEER S, BUHLMANN P, RITOV Y, et al. On asymptotically optimal confidence regions and tests for high dimensional models[J]. The Annals of Statistics, 2014, 42(3): 1166-1202.
|
[16] |
MEINSHAUSEN N. Assumption-free confidence intervals for groups of variables in sparse high-dimensional regression [DB/OL]. [2019-12-01]. https://arxiv.org/abs/1309.3489.
|
[17] |
ZHANG C H, ZHANG S S. Confidence intervals for low-dimensional parameters in high dimensional liner models[J]. Journal of the Royal Statistical Society: Series B, 2014, 76: 217-242.
|
[18] |
JANKOVA J, VAN DE GEER S. Confidence intervals for high-dimensional inverse covariance estimation [J]. Electronic Journal of Statistics, 2015, 9(1): 1205-1229.
|
[19] |
JANKOVA J,VAN DE GEER S. Honest confidence regions and optimality in high-dimensional precision matrix estimation[J]. TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, 2017, 26(1): 143-162.
|
[20] |
HUANG X, LI M. Confidence intervals for sparse precision matrix estimation via Lasso penalized D-trace loss[J]. Communications in Statistics: Theory and Methods, 2017, 46(24): 12299-12316.
|
[21] |
JANKOVA J,VAN DE GEER S. Inference in high dimensional graphical models [DB/OL]. [2019-12-01]. https://arxiv.org/abs/1801.08512.
|
[22] |
YUAN M, LIN Y. Model selection and estimation in the Gaussian graphical model[J]. Biometrika, 2007, 94(1): 19-35.
|
[23] |
STRANGER B E, NICA A C, FORREST M S, et al. Population genomics of human gene expression[J]. Nature Genetics, 2007, 39(10): 1217-1224.
|
[24] |
BHADRA A, MALLICK B K. Joint high-dimensional Bayesian variable and covariance selection with an application to eQTL analysis[J]. Biometrics, 2013, 69(2): 447-457.
|
[25] |
DURRETT R. Probability:Theory and Examples [M]. Cambridge: Cambridge University Press, 2010.
|
[26] |
WANG C, JIANG B. An efficient ADMM algorithm for high dimensional precision matrix estimation via penalized quadratic loss[J]. Computational Statistics & Data Analysis, 2020, 142: Article 106812.
|
[1] |
SCHFER J, STRIMMER K. A shrinkage approach to large-scale covariance matrix estimation and implications for functional genomics[J]. Statistical Applications in Genetics and Molecular Biology, 2005, 4(1): Article 32.
|
[2] |
CHEN X, LIU Y, LIU H, et al. Learning spatial-temporal varying graphs with applications to climate data analysis[C]// Proceedings of the Twenty-Fourth AAAI Conference on Artificial Intelligence. Palo Alto, CA: Association for the Advancement of Artificial Intelligence, 2010: 425-430.
|
[3] |
FAN J, LIAO Y, LIU H. An overview of the estimation of large covariance and precision matrices [J]. Econometrics Journal, 2016, 19(1): C1-C32.
|
[4] |
WAINWRIGHT M J, JORDAN M I. Graphical Models, Exponential Families, and Variational Inference [M]. Hanover,MA: Now, 2008.
|
[5] |
LIU H, LAFFERTY J, WASSERMAN L. The nonparanormal: Semiparametric estimation of high dimensional undirected graphs [J]. Journal of Machine Learning Research, 2009, 10(3): 2295-2328.
|
[6] |
LAURITZEN S. Graphical Models [M]. New York: Oxford Univ Press, 1996.
|
[7] |
MEINSHAUSEN N, BHLMANN P. High-dimensional graphs and variable selection with the Lasso [J]. The Annals of Statistics, 2006, 34(3): 1436-1462.
|
[8] |
BICKEL P J, LEVINA E. Covariance regularization by thresholding[J]. The Annals of Statistics, 2008, 36(6): 2577-2604.
|
[9] |
RAVIKUMAR P, WAINWRIGHT M J, RASKUTTI G, et al. High-dimensional covariance estimation by minimizing 1-penalized log-determinant divergence[J]. Electronic Journal of Statistics, 2011, 5: 935-980.
|
[10] |
LIU W, LUO X. Fast and adaptive sparse precision matrix estimation in high dimensions[J]. Journal of Multivariate Analysis, 2015, 135:153-162.
|
[11] |
REN Z, SUN T, ZHANG C, et al. Asymptotic normality and optimalities in estimation of large Gaussian graphical models[J]. The Annals of Statistics, 2015, 43(3): 991-1026.
|
[12] |
FAN Y, LV J. Innovated scalable efficient estimation in ultra-large Gaussian graphical models[J]. The Annals of Statistics, 2016, 44(5): 2098-2126.
|
[13] |
CAI T, LIU W, LUO X. A constrained 1 minimization approach to sparse precision matrix estimation[J]. Journal of the American Statistical Association, 2011, 106: 594-607.
|
[14] |
NICKL R,VAN DE GEER S. Confidence sets in sparse regression[J]. The Annals of Statistics, 2013, 41(6): 2852-2876.
|
[15] |
VAN DE GEER S, BUHLMANN P, RITOV Y, et al. On asymptotically optimal confidence regions and tests for high dimensional models[J]. The Annals of Statistics, 2014, 42(3): 1166-1202.
|
[16] |
MEINSHAUSEN N. Assumption-free confidence intervals for groups of variables in sparse high-dimensional regression [DB/OL]. [2019-12-01]. https://arxiv.org/abs/1309.3489.
|
[17] |
ZHANG C H, ZHANG S S. Confidence intervals for low-dimensional parameters in high dimensional liner models[J]. Journal of the Royal Statistical Society: Series B, 2014, 76: 217-242.
|
[18] |
JANKOVA J, VAN DE GEER S. Confidence intervals for high-dimensional inverse covariance estimation [J]. Electronic Journal of Statistics, 2015, 9(1): 1205-1229.
|
[19] |
JANKOVA J,VAN DE GEER S. Honest confidence regions and optimality in high-dimensional precision matrix estimation[J]. TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, 2017, 26(1): 143-162.
|
[20] |
HUANG X, LI M. Confidence intervals for sparse precision matrix estimation via Lasso penalized D-trace loss[J]. Communications in Statistics: Theory and Methods, 2017, 46(24): 12299-12316.
|
[21] |
JANKOVA J,VAN DE GEER S. Inference in high dimensional graphical models [DB/OL]. [2019-12-01]. https://arxiv.org/abs/1801.08512.
|
[22] |
YUAN M, LIN Y. Model selection and estimation in the Gaussian graphical model[J]. Biometrika, 2007, 94(1): 19-35.
|
[23] |
STRANGER B E, NICA A C, FORREST M S, et al. Population genomics of human gene expression[J]. Nature Genetics, 2007, 39(10): 1217-1224.
|
[24] |
BHADRA A, MALLICK B K. Joint high-dimensional Bayesian variable and covariance selection with an application to eQTL analysis[J]. Biometrics, 2013, 69(2): 447-457.
|
[25] |
DURRETT R. Probability:Theory and Examples [M]. Cambridge: Cambridge University Press, 2010.
|
[26] |
WANG C, JIANG B. An efficient ADMM algorithm for high dimensional precision matrix estimation via penalized quadratic loss[J]. Computational Statistics & Data Analysis, 2020, 142: Article 106812.
|