Minimax estimation in sparse canonical correlation analysis

Hotelling, H.H. (1936). Relations between two sets of variates. Biometrika 28 321–377

1936

Earlier work this paper cites.

Davis, ChandlerC. andKahan, W. M.W. M. (1970). The rotation of eigenvectors by a perturbation. III. SIAM J. Numer. Anal. 7 1–46

1970

Earlier work this paper cites.

Wedin, Per-ȦkeP.-Ȧ. (1972). Perturbation bounds in connection with singular value decomposition. BIT 12 99–111

1972

Earlier work this paper cites.

LeCam, L.L. (1973). Convergence of estimates under dimensionality restrictions. Ann. Statist. 1 38–53

1973

Earlier work this paper cites.

Mardia, Kantilal VarichandK. V., Kent, John T.J. T. andBibby, John M.J. M. (1979). Multivariate Analysis. Academic Press, London

1979

Earlier work this paper cites.

Birgé, LucienL. (1983). Approximation dans les espaces métriques et théorie de l’estimation. Z. Wahrsch. Verw. Gebiete 65 181–237

1983

Earlier work this paper cites.

Stewart, G. W.G. W. andSun, Ji GuangJ. G. (1990). Matrix Perturbation Theory. Academic Press, Boston, MA

1990

Earlier work this paper cites.

Golub, Gene H.G. H. andVan Loan, Charles F.C. F. (1996). Matrix Computations, 3rd ed. Johns Hopkins Univ. Press, Baltimore, MD

1996

Earlier work this paper cites.

Bhatia, RajendraR. (1997). Matrix Analysis. Graduate Texts in Mathematics 169. Springer, New York

1997

Earlier work this paper cites.

Anderson, T. W.T. W. (1999). Asymptotic theory for canonical correlation analysis. J. Multivariate Anal. 70 1–29

1999

Earlier work this paper cites.

Tipping, Michael E.M. E. andBishop, Christopher M.C. M. (1999). Probabilistic principal component analysis. J. R. Stat. Soc. Ser. B. Stat. Methodol. 61 611–622

1999

Earlier work this paper cites.

Yang, YuhongY. andBarron, AndrewA. (1999). Information-theoretic determination of minimax rates of convergence. Ann. Statist. 27 1564–1599

1999

Earlier work this paper cites.

Johnstone, Iain M.I. M. (2001). On the distribution of the largest eigenvalue in principal components analysis. Ann. Statist. 29 295–327

2001

Earlier work this paper cites.

Anderson, T. W.T. W. (2003). An Introduction to Multivariate Statistical Analysis, 3rd ed. Wiley, Hoboken, NJ

2003

Earlier work this paper cites.

Johnstone, Iain M.I. M. (2008). Multivariate analysis and Jacobi ensembles: Largest eigenvalue, Tracy–Widom limits and rates of convergence. Ann. Statist. 36 2638–2716

2008

Cited alongside, same era.

Wiesel, A.A., Kliger, M.M. andHero, A. O.A. O. III (2008). A greedy approach to sparse canonical correlation analysis. Preprint. Available at \arxivurl

Original

2008

Cited alongside, same era.

Amini, Arash A.A. A. andWainwright, Martin J.M. J. (2009). High-dimensional analysis of semidefinite relaxations for sparse principal components. Ann. Statist. 37 2877–2921

2009

Cited alongside, same era.

Johnstone, Iain M.I. M. andLu, Arthur YuA. Y. (2009). On consistency and sparsity for principal components analysis in high dimensions. J. Amer. Statist. Assoc. 104 682–693

2009

Cited alongside, same era.

Birnbaum, AharonA., Johnstone, Iain M.I. M., Nadler, BoazB. andPaul, DebashisD. (2013). Minimax bounds for sparse PCA with noisy high-dimensional data. Ann. Statist. 41 1055–1084

2013

Later among the works it cites.

Cai, T. TonyT. T., Ma, ZongmingZ. andWu, YihongY. (2013). Sparse PCA: Optimal rates and adaptive estimation. Ann. Statist. 41 3074–3110

2013

Later among the works it cites.

Chen, M.M., Gao, C.C., Ren, Z.Z. andZhou, H. H.H. H. (2013). Sparse CCA via precision adjusted iterative thresholding. Preprint. Available at \arxivurl

Original

2013

Later among the works it cites.

Ma, ZongmingZ. (2013). Sparse principal component analysis and iterative thresholding. Ann. Statist. 41 772–801

2013

Later among the works it cites.

Ma, Z.Z. andWu, Y.Y. (2013). Volume ratio, sparsity, and minimaxity under unitarily invariant norms. Preprint. Available at \arxivurl