In recent years, a considerable amount of work has been devoted to generalizing linear discriminant analysis to overcome its incompetence for high-dimensional classification (Witten and Tibshirani, 2011, Cai and Liu, 2011, Mai et al., 2012 and Fan et al., 2012). In this paper, we develop...

The thresholding covariance estimator has nice asymptotic properties for estimating sparse large covariance matrices, but it often has negative eigenvalues when used in real data analysis. To fix this drawback of thresholding estimation, we develop a positive-definite ℓ₁-penalized covariance...

Cai et al. (2010) [4] have studied the minimax optimal estimation of a collection of large bandable covariance matrices whose off-diagonal entries decay to zero at a polynomial rate. They have shown that the minimax optimal procedures are fundamentally different under Frobenius and spectral...

We propose an efficient and adaptive shrinkage method for variable selection in the Cox model. The method constructs a piecewise-linear regularization path connecting the maximum partial likelihood estimator and the origin. Then a model is selected along the path. We show that the constructed...

We propose the elastic net, a new regularization and variable selection method. Real world data and a simulation study show that the elastic net often outperforms the lasso, while enjoying a similar sparsity of representation. In addition, the elastic net encourages a grouping effect, where...

Bandable covariance matrices are often used to model the dependence structure of variables that follow a nature order. It has been shown that the tapering covariance estimator attains the optimal minimax rates of convergence for estimating large bandable covariance matrices. The estimation risk...