关键词: 高维协方差矩阵, 稳健估计, 中心正则化, 投资组合

Abstract: High-dimensional covariance matrix estimation has become a fundamental problem in big-data statistical analysis.Traditional methods require data to be normally distributed without considering the influence of outliers.At present,they cannot meet the needs of application.More robust methods need to be proposed.For high-dimensional covariance matrices,a robust mean-median estimation method based on sub-sample grouping is proposed and easy to use.However, the matrix estimated by this method is not positive-definite and sparse.Motivated by this problem, this paper introduces a central-regularized algorithm to avoid the shortcomings of the original method.By imposing L1 norm penalty on the off-diagonal elements of the estimated matrix,the estimated matrix could be positive-definite and sparse,thus greatly improving its application value.In the numerical simulation,the central-regularized estimation proposed in this paper has higher estimation accuracy,and is closer to the sparse structure of the real set matrix.In the subsequent empirical analysis of portfolios,the minimum variance portfolio based on central-regularized estimator has the lowest volatility,which outperforms traditional sample covariance matrix estimation method,mean-median estimation method and RALASSO method.

Key words: High-dimensional Covariance Matrix, Robust Estimation, Central-Regularized, Portfolio Selection