Positive-Definite ℓ 1 -Penalized Estimation of Large Covariance Matrices
大型协方差矩阵的正定 ℓ1 惩罚估计
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 estimator for estimating sparse large covariance matrices. We derive an efficient alternating direction method to solve the challenging optimization problem and establish its convergence…