Estimating Structured High-Dimensional Covariance and Precision Matrices: Optimal Rates and Adaptive Estimation
Tony Cai, Zhao Ren, and Harrison Zhou
Cai, T., Zhang, C.-H. & Zhou, H. (2010).
Optimal rates of convergence for covariance matrix estimation.
The Annals of Statistics 38, 2118-2144.
Cai, T. T. & Jiang, T. (2011).
Limiting laws of coherence of random matrices with applications to testing covariance structure and construction of compressed sensing matrices.
The Annals of Statistics 39, 1496-1525.
Cai, T. & Liu, W. (2011).
Adaptive thresholding for sparse covariance matrix estimation.
J. American Statistical Association 106, 672-684.
Cai, T. T. & Liu, W. (2011).
A direct estimation approach to sparse linear discriminant analysis.
Journal of the American Statistical Association 106, 1566-1577.
Cai, T., Liu, W. & Luo, X. (2011).
A constrained l_{1} minimization approach to sparse precision matrix estimation.
J. American Statistical Association 494, 594-607.
Cai, T. T., Liu, W. & Zhou, H. (2012).
Estimating sparse precision matrix: Optimal rates of convergence and adaptive estimation.
The Annals of Statistics, to appear.
Cai, T. & Yuan, M. (2012).
Adaptive covariance matrix estimation through block thresholding.
The Annals of Statistics 40, 2014-2042.
Cai, T. & Zhou, H. (2012).
Optimal rates of convergence for sparse covariance matrix estimation.
The Annals of Statistics 40, 2389-2420.
Cai, T. T. & Zhou, H. (2012).
Minimax estimation of large covariance matrices under l_{1} norm (with discussion).
Statistica Sinica 22, 1319-1378.
Cai, T. T., Liang, T. & Zhou, H. (2013).
Law of log determinant of sample covariance matrix and optimal estimation of differential entropy for high-dimensional Gaussian distributions.
Technical report.
Cai, T. T., Liu, W. & Xia, Y. (2013).
Two-sample covariance matrix testing and support recovery in high-dimensional and sparse settings.
Journal of the American Statistical Association 108, 265-277.
Cai, T. T. & Ma, Z. (2013).
Optimal hypothesis testing for high dimensional covariance matrices.
Bernoulli 19, 2359-2388.
Cai, T. T., Ma, Z. & Wu, Y. (2013).
Sparse PCA: Optimal rates and adaptive estimation.
The Annals of Statistics 41, 3074-3110.
Cai, T. T., Ma, Z. & Wu, Y. (2013).
Optimal estimation and rank detection for sparse spiked covariance matrices.
Probability Theory and Related Fields, to appear.
Cai, T. T., Ren, Z. & Zhou, H. (2013).
Optimal rates of convergence for estimating Toeplitz covariance matrices.
Probability Theory and Related Fields 156, 101-143.