High-Dimensional Covariance Estimation via Constrained Lq-Type Regularization

High-dimensional covariance matrix estimation is one of the fundamental and important problems in multivariate analysis has a wide range applications many fields. In practice, it common that composed low-rank sparse matrix. this paper we estimate by solving constrained Lq-type regularized optimization problem. We establish first-order optimality conditions for problem using proximal mapping subspace method. The proposed stationary point degenerates to points unconstrained Lq or problems. A smoothing alternating updating method find an estimator convergence calculation numerical simulation results show effectiveness approach high-dimensional estimation.