[1] |
Baselmans B M, Jansen R, Ip H F, et al. Multivariate genome-wide analyses of the well-being spectrum. Nature Genetics, 2019, 51 (3): 445–451. doi: 10.1038/s41588-018-0320-8
|
[2] |
Yang K, Lee L F. Identification and QML estimation of multivariate and simultaneous equations spatial autoregressive models. Journal of Econometrics, 2017, 196 (1): 196–214. doi: 10.1016/j.jeconom.2016.04.019
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[3] |
Zhu X, Huang D, Pan R, et al. Multivariate spatial autoregressive model for large scale social networks. Journal of Econometrics, 2020, 215 (2): 591–606. doi: 10.1016/j.jeconom.2018.11.018
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[4] |
Han F, Liu H. Optimal rates of convergence for latent generalized correlation matrix estimation in transelliptical distribution. arXiv: 1305.6916, 2013.
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[5] |
Rubinstein M. Markowitz’s “portfolio selection”: A fifty-year retrospective. The Journal of Finance, 2002, 57 (3): 1041–1045. doi: 10.1111/1540-6261.00453
|
[6] |
Wegkamp M, Zhao Y. Adaptive estimation of the copula correlation matrix for semiparametric elliptical copulas. Bernoulli, 2016, 22 (2): 1184–1226. doi: 10.3150/14-BEJ690
|
[7] |
Fan J, Han F, Liu H. Challenges of big data analysis. National Science Review, 2014, 1 (2): 293–314. doi: 10.1093/nsr/nwt032
|
[8] |
Cai T, Liu W, Luo X. A constrained ℓ1 minimization approach to sparse precision matrix estimation. Journal of the American Statistical Association, 2011, 106 (494): 594–607. doi: 10.1198/jasa.2011.tm10155
|
[9] |
Tokuda T, Goodrich B, van Mechelen I, et al. Visualizing distributions of covariance matrices. New York: Columbia University, 2011.
|
[10] |
Fan J, Peng H. Nonconcave penalized likelihood with a diverging number of parameters. The Annals of Statistics, 2004, 32 (3): 928–961. doi: 10.1214/009053604000000256
|
[11] |
Yuan M, Lin Y. Model selection and estimation in the Gaussian graphical model. Biometrika, 2007, 94 (1): 19–35. doi: 10.1093/biomet/asm018
|
[12] |
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
|
[13] |
Banerjee O, El Ghaoui L, d’Aspremont A. Model selection through sparse maximum likelihood estimation for multivariate Gaussian or binary data. The Journal of Machine Learning Research, 2008, 9: 485–516. doi: 10.5555/1390681.1390696
|
[14] |
Meinshausen N, Bühlmann P. High-dimensional graphs and variable selection with the Lasso. The Annals of Statistics, 2006, 34 (3): 1436–1462. doi: 10.1214/009053606000000281
|
[15] |
Wille A, Zimmermann P, Vranova E, et al. Sparse graphical Gaussian modeling of the isoprenoid gene network in Arabidopsis thaliana. Genome Biology, 2004, 5 (11): R92. doi: 10.1186/gb-2004-5-11-r92
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[16] |
Rothman A J, Bickel P J, Levina E, et al. Sparse permutation invariant covariance estimation. Electronic Journal of Statistics, 2008, 2: 494–515. doi: 10.1214/08-EJS176
|
[17] |
Lam C, Fan J. Sparsistency and rates of convergence in large covariance matrix estimation. The Annals of Statistics, 2009, 37 (6B): 4254–4278. doi: 10.1214/09-AOS720
|
[18] |
Yuan M. High dimensional inverse covariance matrix estimation via linear programming. The Journal of Machine Learning Research, 2010, 11: 2261–2286. doi: 10.5555/1756006.1859930
|
[19] |
Liu W, Luo X. High-dimensional sparse precision matrix estimation via sparse column inverse operator. arXiv: 1203.3896, 2012.
|
[20] |
Sun T, Zhang C H. Sparse matrix inversion with scaled Lasso. The Journal of Machine Learning Research, 2013, 14 (1): 3385–3418. doi: 10.5555/2567709.2567771
|
[21] |
Fan Y, Lv J. Innovated scalable efficient estimation in ultra-large Gaussian graphical models. The Annals of Statistics, 2016, 44 (5): 2098–2126. doi: 10.1214/15-AOS1416
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[22] |
Bickel P, Ritov Y. Efficient estimation in the errors in variables model. The Annals of Statistics, 1987, 15 (2): 513–540. doi: 10.1214/aos/1176350358
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[23] |
Ma Y, Li R. Variable selection in measurement error models. Bernoulli, 2010, 16 (1): 274–300. doi: 10.3150/09-bej205
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[24] |
Liang H, Li R. Variable selection for partially linear models with measurement errors. Journal of the American Statistical Association, 2009, 104 (485): 234–248. doi: 10.1198/jasa.2009.0127
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[25] |
Städler N, Bühlmann P. Missing values: Sparse inverse covariance estimation and an extension to sparse regression. Statistics and Computing, 2012, 22 (1): 219–235. doi: 10.1007/s11222-010-9219-7
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[26] |
Loh P L, Wainwright M J. High-dimensional regression with noisy and missing data: Provable guarantees with nonconvexity. Advances in Neural Information Processing Systems, 2012, 40 (3): 1637–1664. doi: 10.1214/12-AOS1018
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[27] |
Belloni A, Rosenbaum M, Tsybakov A B. Linear and conic programming estimators in high dimensional errors-in-variables models. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 2017, 79 (3): 939–956. doi: 10.1111/rssb.12196
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[28] |
Datta A, Zou H. Cocolasso for high-dimensional error-in-variables regression. The Annals of Statistics, 2017, 45 (6): 2400–2426. doi: 10.1214/16-AOS1527
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[29] |
Tibshirani R. Regression shrinkage and selection via the Lasso. Journal of the Royal Statistical Society: Series B (Methodological), 1996, 58 (1): 267–288. doi: 10.1111/j.2517-6161.1996.tb02080.x
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[30] |
Fan J, Li R. Variable selection via nonconcave penalized likelihood and its oracle properties. Journal of the American Statistical Association, 2001, 96 (456): 1348–1360. doi: 10.1198/016214501753382273
|
[31] |
Zou H, Hastie T. Regularization and variable selection via the elastic net. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 2005, 67 (2): 301–320. doi: 10.1111/j.1467-9868.2005.00503.x
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[32] |
Zou H. The adaptive Lasso and its oracle properties. Journal of the American Statistical Association, 2006, 101 (476): 1418–1429. doi: 10.1198/016214506000000735
|
[33] |
Candes E, Tao T. The Dantzig selector: Statistical estimation when p is much larger than n. The Annals of Statistics, 2007, 35 (6): 2313–2351. doi: 10.1214/009053606000001523
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[34] |
Bickel P J, Ritov Y, Tsybakov A B. Simultaneous analysis of Lasso and Dantzig selector. The Annals of Statistics, 2009, 37 (4): 1705–1732. doi: 10.1214/08-AOS620
|
[35] |
Zhao P, Yu B. On model selection consistency of Lasso. The Journal of Machine Learning Research, 2006, 7: 2541–2563. doi: 10.5555/1248547.1248637
|
[36] |
Wainwright M J. Sharp thresholds for high-dimensional and noisy sparsity recovery using l1-constrained quadratic programming (Lasso). IEEE Transactions on Information Theory, 2009, 55 (5): 2183–2202. doi: 10.1109/TIT.2009.2016018
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[37] |
Buldygin V V, Kozachenko Yu V. Metric Characterization of Random Variables and Random Processes. Providence, RI: American Mathematical Society, 2000.
|
[38] |
Sun T, Zhang C H. Scaled sparse linear regression. Biometrika, 2012, 99 (4): 879–898. doi: 10.1093/biomet/ass043
|
[39] |
Ren Z, Sun T, Zhang C H, et al. Asymptotic normality and optimalities in estimation of large Gaussian graphical models. The Annals of Statistics, 2015, 43 (3): 991–1026. doi: 10.1214/14-AOS1286
|
[40] |
Bickel P J, Levina E. Regularized estimation of large covariance matrices. The Annals of Statistics, 2008, 36 (1): 199–227. doi: 10.1214/009053607000000758
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[41] |
Bickel P J, Levina E. Covariance regularization by thresholding. The Annals of Statistics, 2008, 36 (6): 2577–2604. doi: 10.1214/08-AOS600
|
[1] |
Baselmans B M, Jansen R, Ip H F, et al. Multivariate genome-wide analyses of the well-being spectrum. Nature Genetics, 2019, 51 (3): 445–451. doi: 10.1038/s41588-018-0320-8
|
[2] |
Yang K, Lee L F. Identification and QML estimation of multivariate and simultaneous equations spatial autoregressive models. Journal of Econometrics, 2017, 196 (1): 196–214. doi: 10.1016/j.jeconom.2016.04.019
|
[3] |
Zhu X, Huang D, Pan R, et al. Multivariate spatial autoregressive model for large scale social networks. Journal of Econometrics, 2020, 215 (2): 591–606. doi: 10.1016/j.jeconom.2018.11.018
|
[4] |
Han F, Liu H. Optimal rates of convergence for latent generalized correlation matrix estimation in transelliptical distribution. arXiv: 1305.6916, 2013.
|
[5] |
Rubinstein M. Markowitz’s “portfolio selection”: A fifty-year retrospective. The Journal of Finance, 2002, 57 (3): 1041–1045. doi: 10.1111/1540-6261.00453
|
[6] |
Wegkamp M, Zhao Y. Adaptive estimation of the copula correlation matrix for semiparametric elliptical copulas. Bernoulli, 2016, 22 (2): 1184–1226. doi: 10.3150/14-BEJ690
|
[7] |
Fan J, Han F, Liu H. Challenges of big data analysis. National Science Review, 2014, 1 (2): 293–314. doi: 10.1093/nsr/nwt032
|
[8] |
Cai T, Liu W, Luo X. A constrained ℓ1 minimization approach to sparse precision matrix estimation. Journal of the American Statistical Association, 2011, 106 (494): 594–607. doi: 10.1198/jasa.2011.tm10155
|
[9] |
Tokuda T, Goodrich B, van Mechelen I, et al. Visualizing distributions of covariance matrices. New York: Columbia University, 2011.
|
[10] |
Fan J, Peng H. Nonconcave penalized likelihood with a diverging number of parameters. The Annals of Statistics, 2004, 32 (3): 928–961. doi: 10.1214/009053604000000256
|
[11] |
Yuan M, Lin Y. Model selection and estimation in the Gaussian graphical model. Biometrika, 2007, 94 (1): 19–35. doi: 10.1093/biomet/asm018
|
[12] |
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
|
[13] |
Banerjee O, El Ghaoui L, d’Aspremont A. Model selection through sparse maximum likelihood estimation for multivariate Gaussian or binary data. The Journal of Machine Learning Research, 2008, 9: 485–516. doi: 10.5555/1390681.1390696
|
[14] |
Meinshausen N, Bühlmann P. High-dimensional graphs and variable selection with the Lasso. The Annals of Statistics, 2006, 34 (3): 1436–1462. doi: 10.1214/009053606000000281
|
[15] |
Wille A, Zimmermann P, Vranova E, et al. Sparse graphical Gaussian modeling of the isoprenoid gene network in Arabidopsis thaliana. Genome Biology, 2004, 5 (11): R92. doi: 10.1186/gb-2004-5-11-r92
|
[16] |
Rothman A J, Bickel P J, Levina E, et al. Sparse permutation invariant covariance estimation. Electronic Journal of Statistics, 2008, 2: 494–515. doi: 10.1214/08-EJS176
|
[17] |
Lam C, Fan J. Sparsistency and rates of convergence in large covariance matrix estimation. The Annals of Statistics, 2009, 37 (6B): 4254–4278. doi: 10.1214/09-AOS720
|
[18] |
Yuan M. High dimensional inverse covariance matrix estimation via linear programming. The Journal of Machine Learning Research, 2010, 11: 2261–2286. doi: 10.5555/1756006.1859930
|
[19] |
Liu W, Luo X. High-dimensional sparse precision matrix estimation via sparse column inverse operator. arXiv: 1203.3896, 2012.
|
[20] |
Sun T, Zhang C H. Sparse matrix inversion with scaled Lasso. The Journal of Machine Learning Research, 2013, 14 (1): 3385–3418. doi: 10.5555/2567709.2567771
|
[21] |
Fan Y, Lv J. Innovated scalable efficient estimation in ultra-large Gaussian graphical models. The Annals of Statistics, 2016, 44 (5): 2098–2126. doi: 10.1214/15-AOS1416
|
[22] |
Bickel P, Ritov Y. Efficient estimation in the errors in variables model. The Annals of Statistics, 1987, 15 (2): 513–540. doi: 10.1214/aos/1176350358
|
[23] |
Ma Y, Li R. Variable selection in measurement error models. Bernoulli, 2010, 16 (1): 274–300. doi: 10.3150/09-bej205
|
[24] |
Liang H, Li R. Variable selection for partially linear models with measurement errors. Journal of the American Statistical Association, 2009, 104 (485): 234–248. doi: 10.1198/jasa.2009.0127
|
[25] |
Städler N, Bühlmann P. Missing values: Sparse inverse covariance estimation and an extension to sparse regression. Statistics and Computing, 2012, 22 (1): 219–235. doi: 10.1007/s11222-010-9219-7
|
[26] |
Loh P L, Wainwright M J. High-dimensional regression with noisy and missing data: Provable guarantees with nonconvexity. Advances in Neural Information Processing Systems, 2012, 40 (3): 1637–1664. doi: 10.1214/12-AOS1018
|
[27] |
Belloni A, Rosenbaum M, Tsybakov A B. Linear and conic programming estimators in high dimensional errors-in-variables models. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 2017, 79 (3): 939–956. doi: 10.1111/rssb.12196
|
[28] |
Datta A, Zou H. Cocolasso for high-dimensional error-in-variables regression. The Annals of Statistics, 2017, 45 (6): 2400–2426. doi: 10.1214/16-AOS1527
|
[29] |
Tibshirani R. Regression shrinkage and selection via the Lasso. Journal of the Royal Statistical Society: Series B (Methodological), 1996, 58 (1): 267–288. doi: 10.1111/j.2517-6161.1996.tb02080.x
|
[30] |
Fan J, Li R. Variable selection via nonconcave penalized likelihood and its oracle properties. Journal of the American Statistical Association, 2001, 96 (456): 1348–1360. doi: 10.1198/016214501753382273
|
[31] |
Zou H, Hastie T. Regularization and variable selection via the elastic net. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 2005, 67 (2): 301–320. doi: 10.1111/j.1467-9868.2005.00503.x
|
[32] |
Zou H. The adaptive Lasso and its oracle properties. Journal of the American Statistical Association, 2006, 101 (476): 1418–1429. doi: 10.1198/016214506000000735
|
[33] |
Candes E, Tao T. The Dantzig selector: Statistical estimation when p is much larger than n. The Annals of Statistics, 2007, 35 (6): 2313–2351. doi: 10.1214/009053606000001523
|
[34] |
Bickel P J, Ritov Y, Tsybakov A B. Simultaneous analysis of Lasso and Dantzig selector. The Annals of Statistics, 2009, 37 (4): 1705–1732. doi: 10.1214/08-AOS620
|
[35] |
Zhao P, Yu B. On model selection consistency of Lasso. The Journal of Machine Learning Research, 2006, 7: 2541–2563. doi: 10.5555/1248547.1248637
|
[36] |
Wainwright M J. Sharp thresholds for high-dimensional and noisy sparsity recovery using l1-constrained quadratic programming (Lasso). IEEE Transactions on Information Theory, 2009, 55 (5): 2183–2202. doi: 10.1109/TIT.2009.2016018
|
[37] |
Buldygin V V, Kozachenko Yu V. Metric Characterization of Random Variables and Random Processes. Providence, RI: American Mathematical Society, 2000.
|
[38] |
Sun T, Zhang C H. Scaled sparse linear regression. Biometrika, 2012, 99 (4): 879–898. doi: 10.1093/biomet/ass043
|
[39] |
Ren Z, Sun T, Zhang C H, et al. Asymptotic normality and optimalities in estimation of large Gaussian graphical models. The Annals of Statistics, 2015, 43 (3): 991–1026. doi: 10.1214/14-AOS1286
|
[40] |
Bickel P J, Levina E. Regularized estimation of large covariance matrices. The Annals of Statistics, 2008, 36 (1): 199–227. doi: 10.1214/009053607000000758
|
[41] |
Bickel P J, Levina E. Covariance regularization by thresholding. The Annals of Statistics, 2008, 36 (6): 2577–2604. doi: 10.1214/08-AOS600
|