统计与决策2026，Vol.42Issue(3)：59-65,7.DOI:10.13546/j.cnki.tjyjc.2026.03.010
基于Log-Median方法的协方差矩阵估计方法及应用
Covariance Matrix Estimation Method Based on Log-Median Method and Its Applications
吴雪柔 1赵寿为1
作者信息
- 1. 上海工程技术大学 数理与统计学院,上海 201620
- 折叠
摘要
Abstract
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.关键词
协方差矩阵估计/负对数似然函数/特征值中位数/惩罚项Key words
covariance matrix estimation/negative log-likelihood function/median of eigenvalues/penalty term分类
数理科学引用本文复制引用
吴雪柔,赵寿为..基于Log-Median方法的协方差矩阵估计方法及应用[J].统计与决策,2026,42(3):59-65,7.
