Low rank multivariate regression

Electronic Journal of Statistics

Volumn 5, Issue , 2011, Pages 775-799

  Giraud, Christophe ^a  

^a CENTRE DE MATHÉMATIQUES APPLIQUÉES   (France)

Author keywords

Estimator selection; Ky Fan norms; Multivariate regression; Random matrix

Indexed keywords

EID: 82655164897     PISSN: 19357524     EISSN: None     Source Type: Journal    
DOI: 10.1214/11-EJS625     Document Type: Article

References (23)

1. T.W. Anderson. Estimating linear restrictions on regression coefficients for multivariate normal distribution. Annals of Mathematical Statistics 22 (1951), 327-351. MR0042664
2. C.W. Anderson, E.A. Stolz, and S. Shamsunder. Multivariate autoregressive models for classification of spontaneous electroencephalogram during mental tasks. IEEE Trans. on bio-medical engineering, 45 no 3 (1998), 277-286.
3. F. Bach. Consistency of trace norm minimization, Journal of Machine Learning Research, 9 (2008), 1019-1048. MR2417263
4. Y. Baraud, C. Giraud and S. Huet. Estimator selection in the Gaussian setting. arXiv:1007.2096v2
5. L. Birgé and P. Massart. Minimal penalties for Gaussian model selection. Probability Theory and Related Fields, 138 no 1-2 (2007), 33-73. MR2288064
6. E.N. Brown, R.E. Kass, and P.P. Mitra. Multiple neural spike train data analysis: state-of-the-art and future challenges. Nature Neuroscience, 7 no 5 (2004), 456-461.
7. F. Bunea, Y. She and M. Wegkamp. Adaptive rank Penalized Estimators in Multivariate Regression. arXiv:1004.2995v1 (2010)
8. F. Bunea, Y. She and M. Wegkamp. Optimal selection of reduced rank estimation of high-dimensional matrices. To appear in the Annals of Statist.
9. Davidson and Szarek. Handbook of the Geometry of Banach Spaces. North-Holland Publishing Co., Amsterdam, 2001.
10. C. Giraud. Low rank multivariate regression. arXiv:1009.5165v1 (Sept. 2010)
11. C. Giraud. A pseudo RIP for multivariate regression. arXiv:1106.5599v1 (2011)
12. L. Harrison, W.D. Penny, and K. Friston. Multivariate autoregressive modeling of fmri time series. NeuroImage, 19 (2004), 1477-1491
13. R.A. Horn and C.R. Johnson. Topics in Matrix Analysis. Cambridge University Press, Cambridge, 1994. MR1288752
14. A.J. Izenman. Reduced-rank regression for the multivariate linear model. Journal of Multivariate analysis 5 (1975), 248-262. MR0373179
15. A.J. Izenman. Modern Multivariate Statistical Techniques: Regression, Classification, and Manifold Learning. Springer, New York, 2008. MR2445017
16. V. Koltchinskii, A. Tsybakov and K. Lounici. Nuclear norm penalization and optimal rates for noisy low rank matrix completion. To appear in the Annals of Statist. MR2329462
17. M. Ledoux. The concentration of measure phenomenon. Mathematical Surveys and Monographs, 89. American Mathematical Society, Providence, 2001. MR1849347
18. Z. Lu, R. Monteiro and M. Yuan. Convex optimization methods for dimension reduction and coefficient estimation in multivariate linear regression. Mathematical Programming (to appear).
19. V. A. Marchenko, L.A. Pastur. Distribution of eigenvalues for some sets of random matrices. Mat. Sb. (N.S.), 72(114):4 (1967), 507-536. MR0208649
20. S. Negahban and M.J. Wainwright. Estimation of (near) low-rank matrices with noise and high-dimensional scaling. Annals of Statist. 39 (2011), no. 2, 1069-1097.
21. A. Rohde, A.B. Tsybakov. Estimation of High-Dimensional Low-Rank Matrices. Ann. Statist. Volume 39, Number 2 (2011), 887-930.
22. M. Rudelson, R. Vershynin. Non-asymptotic theory of random matrices: Extreme singular values. Proceedings of the International Congress of Mathematicians, Hyderabad, India, (2010).
23. M. Yuan, A. Ekici, Z. Lu and R. Monteiro. Dimension Reduction and Coefficient Estimation in Multivariate Linear Regression. Journal of the Royal Statistical Society, Series B, 69 (2007), 329-346. MR2323756