[1] |
YUAN M, EKICI A, LU Z, et al. Dimension reduction and coefficient estimation in multivariate linear regression[J]. Journal of the Royal Statistical Society, 2010, 57(3): 329-346.
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[2] |
NEGAHBAN S N, WAINWRIGHT M J. Estimation of (near) low-rank matrices with noise and high-dimensional scaling[J]. International Conference on Machine Learning, 2010, 39(2): 823-830.
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[3] |
BUNEA F, SHE Y, WEGKAMP M H. Optimal selection of reduced rank estimators of high-dimensional matrices[J]. Annals of Statistics, 2010, 39(2): 1282-1309.
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[4] |
CHEN K, DONG H, CHAN K S. Reduced rank regression via adaptive nuclear norm penalization[J]. Biometrika, 2013, 100(4): 901-920.
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[5] |
FAN J, LI R. Variable selection vianonconvave penalized likelihood and its oracle properties[J]. Publications of the American Statistical Association, 2001, 96(456): 1348-1360.
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[6] |
ZHENG Z, FAN Y, LV J. High dimensional thresholded regression and shrinkage effect[J].Journal of the Royal Statistical Society B, 2014, 76(3) : 627-649.
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[7] |
HOERL A E, KENNARDR W. Ridge regression: Biased estimation for nonorthogonal problems[J]. Technometrics, 2000, 42(1): 80-86.
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[8] |
ROHDE A, TSYBAKOV A B. Estimation of high-dimensional low-rank matrices[J]. Annals of Statistics, 2011, 39(2): 887-930.
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[9] |
DONOHO D L, ELAD M. Optimally sparse representation in general (nonorthogonal) dictionaries via l minimization[J]. Proceedings of the National Academy of Sciences of the United States of America, 2003, 100(5): 2197-2202.
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[10] |
BICKEL P J, RITOV Y, TSYBAKOV A B. Simultaneous analysis of lasso and Dantzig selector[J]. Annals of Statistics, 2008, 37(4): 1705-1732.
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[11] |
FAN J, LV J.Nonconcave penalized likelihood with NP-dimensionality[J]. IEEE Transactions on Information Theory, 2011, 57(8): 5467-5484.
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[12] |
REINSEL G C, VELU R P. Multivariate Reduced-Rank Regression[M]. New York: Springer, 1998: 369-370.
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[13] |
ZOU H, LI R. One-step sparse estimates innonconcave penalized likelihood models[J]. Annals of Statistics, 2008, 36(4): 1509-1533.
|
[14] |
LANGE K, HUNTER D R, YANG I. Optimization transfer using surrogate objective functions[J]. Journal of Computational and Graphical Statistics, 2000, 9(1): 1-20.
|
[15] |
ZOU H, HASTIE T. Regularization and variable selection via the elastic net[J]. J Roy Statist Soc Ser B, 2005, 67(2): 301-320.
|
[16] |
TIBSHIRANI R. Regression shrinkage and selection via the lasso[J]. Journal of the Royal Statistical Society, 2011, 73(3): 273-282.
|
[17] |
HUANG J, HOROWITZ J L, MA S. Asymptotic properties of bridge estimators in sparse high-dimensional regression models[J]. Annals of Statistics, 2008, 36(2): 587-613.
|
[18] |
KLOPP O. Rank penalized estimators for high-dimensional matrices[J]. Electronic Journal of Statistics, 2011, 5(2011): 1161-1183.
|
[19] |
KOLTCHINSKII V, LOUNICI K, TSYBAKOV A B. Nuclear-norm penalization and optimal rates for noisy low-rank matrix completion[J]. Annals of Statistics, 2011, 39(5): 2302-2329.
|
[20] |
WITTEN D M, TIBSHIRANI R, HASTIE T. A penalized matrix decomposition, with applications to sparse principal components and canonical correlation analysis[J]. Biostatistics, 2009, 10(3): 515-534.
|
[21] |
CHIN K, DEVRIES S, FRIDLYAND J, et al. Genomic and transcriptional aberrations linked to breast cancer pathophysiologies[J]. Cancer Cell, 2006, 10(6): 529-541.
|
[22] |
VON NEUMANN J. Some matrix-inequalities and metrization of matrix-space[J]. Tomsk Univ Rev, 1937, 11(1): 286-300.
|
[1] |
YUAN M, EKICI A, LU Z, et al. Dimension reduction and coefficient estimation in multivariate linear regression[J]. Journal of the Royal Statistical Society, 2010, 57(3): 329-346.
|
[2] |
NEGAHBAN S N, WAINWRIGHT M J. Estimation of (near) low-rank matrices with noise and high-dimensional scaling[J]. International Conference on Machine Learning, 2010, 39(2): 823-830.
|
[3] |
BUNEA F, SHE Y, WEGKAMP M H. Optimal selection of reduced rank estimators of high-dimensional matrices[J]. Annals of Statistics, 2010, 39(2): 1282-1309.
|
[4] |
CHEN K, DONG H, CHAN K S. Reduced rank regression via adaptive nuclear norm penalization[J]. Biometrika, 2013, 100(4): 901-920.
|
[5] |
FAN J, LI R. Variable selection vianonconvave penalized likelihood and its oracle properties[J]. Publications of the American Statistical Association, 2001, 96(456): 1348-1360.
|
[6] |
ZHENG Z, FAN Y, LV J. High dimensional thresholded regression and shrinkage effect[J].Journal of the Royal Statistical Society B, 2014, 76(3) : 627-649.
|
[7] |
HOERL A E, KENNARDR W. Ridge regression: Biased estimation for nonorthogonal problems[J]. Technometrics, 2000, 42(1): 80-86.
|
[8] |
ROHDE A, TSYBAKOV A B. Estimation of high-dimensional low-rank matrices[J]. Annals of Statistics, 2011, 39(2): 887-930.
|
[9] |
DONOHO D L, ELAD M. Optimally sparse representation in general (nonorthogonal) dictionaries via l minimization[J]. Proceedings of the National Academy of Sciences of the United States of America, 2003, 100(5): 2197-2202.
|
[10] |
BICKEL P J, RITOV Y, TSYBAKOV A B. Simultaneous analysis of lasso and Dantzig selector[J]. Annals of Statistics, 2008, 37(4): 1705-1732.
|
[11] |
FAN J, LV J.Nonconcave penalized likelihood with NP-dimensionality[J]. IEEE Transactions on Information Theory, 2011, 57(8): 5467-5484.
|
[12] |
REINSEL G C, VELU R P. Multivariate Reduced-Rank Regression[M]. New York: Springer, 1998: 369-370.
|
[13] |
ZOU H, LI R. One-step sparse estimates innonconcave penalized likelihood models[J]. Annals of Statistics, 2008, 36(4): 1509-1533.
|
[14] |
LANGE K, HUNTER D R, YANG I. Optimization transfer using surrogate objective functions[J]. Journal of Computational and Graphical Statistics, 2000, 9(1): 1-20.
|
[15] |
ZOU H, HASTIE T. Regularization and variable selection via the elastic net[J]. J Roy Statist Soc Ser B, 2005, 67(2): 301-320.
|
[16] |
TIBSHIRANI R. Regression shrinkage and selection via the lasso[J]. Journal of the Royal Statistical Society, 2011, 73(3): 273-282.
|
[17] |
HUANG J, HOROWITZ J L, MA S. Asymptotic properties of bridge estimators in sparse high-dimensional regression models[J]. Annals of Statistics, 2008, 36(2): 587-613.
|
[18] |
KLOPP O. Rank penalized estimators for high-dimensional matrices[J]. Electronic Journal of Statistics, 2011, 5(2011): 1161-1183.
|
[19] |
KOLTCHINSKII V, LOUNICI K, TSYBAKOV A B. Nuclear-norm penalization and optimal rates for noisy low-rank matrix completion[J]. Annals of Statistics, 2011, 39(5): 2302-2329.
|
[20] |
WITTEN D M, TIBSHIRANI R, HASTIE T. A penalized matrix decomposition, with applications to sparse principal components and canonical correlation analysis[J]. Biostatistics, 2009, 10(3): 515-534.
|
[21] |
CHIN K, DEVRIES S, FRIDLYAND J, et al. Genomic and transcriptional aberrations linked to breast cancer pathophysiologies[J]. Cancer Cell, 2006, 10(6): 529-541.
|
[22] |
VON NEUMANN J. Some matrix-inequalities and metrization of matrix-space[J]. Tomsk Univ Rev, 1937, 11(1): 286-300.
|