Abstract: Aiming at the problem of sparse covariance matrix estimation, we proposed a sparse covariance matrix estimator based on the MCP (minimax concave penalty) penalized log-likelihood, and solved it by using  the coordinate descent algorithm. The simulation results show that the proposed method can achieve  smaller L₁ norms, Kullback-Leibler distances, and Frobenius norms compared to the Lasso penalty and SCAD (smoothly clipped absolute deviation) penalty methods when estimating sparse covariance matrices in most cases, especially under the AR(1) model setting, the performance is more outstanding. In addition, the superior performance of the MCP penalty method for practical applications is verified by analyzing the protein concentration data measured by flow cytometry.

Key words:  , covariance matrix, MCP penalty, coordinate descent algorithm, sparse estimation