基于Log-Median方法的协方差矩阵估计方法及应用OACHSSCD

In the field of data analysis and statistical modeling,the accuracy of covariance matrix estimation is of vital impor-tance.However,traditional estimation methods often fail to provide accurate estimation results when confronted with outliers inter-fering with data models or distribution skewness.In order to address the above problem,this paper proposes a novel covariance matrix estimation method—Log-Median method.This method initially constructs the negative log-likelihood function of the cova-riance matrix,and then estimates the median of eigenvalues by incorporating a linear regression model.Finally,it introduces a penalty term to regularize the abnormal eigenvalues in the covariance matrix estimation towards the median of eigenvalues,achiev-ing stability in covariance matrix estimation.Both simulation studies of six data models and empirical analysis of stock data and categorical data demonstrate that the Log-Median method exhibits excellent performance under various data environments,en-hancing the accuracy and robustness of covariance matrix estimation results.