基于交叉验证收缩法的高维协方差矩阵估计  

Estimation of High Dimensional Covariance Matrix Based on Cross-Validation Shrinkage Method

作　　者：刘恒 郭精军 Liu Heng;Guo Jingjun(School of Statistics,Lanzhou University of Finance and Economics,Lanzhou 730020,China)

机构地区：[1]兰州财经大学统计学院,兰州730020

出　　处：《统计与决策》2020年第9期39-42,共4页Statistics & Decision

基　　金：国家自然科学基金资助项目(71561017;71961013)。

摘　　要：协方差矩阵及其逆矩阵的估计研究在通信工程、金融等领域中有着重要的应用价值。文章将样本协方差矩阵与其锥形(Tapering)矩阵进行凸线性组合,用交叉验证的方法研究了高维数据背景下协方差矩阵的估计问题。首先确定了Tapering矩阵未知时的最优窗宽,得到了未知收缩强度的显式解。其次提出了新的协方差矩阵估计量——交叉验证收缩估计量(CVS)。结果发现:将其应用在估计区间较大的投资组合时,CVS估计量使投资者获得了更高的收益和经济福利。The estimation of covariance matrix and its inverse matrix has important application value in communication engineering,finance and other fields.This paper carries out a convex linear combination of sample covariance matrix and Tapering matrix,using means of cross validation to study the estimation of covariance matrix in the background of high-dimensional data.First,the optimal window width when the[Tapering]matrix is unknown is determined to obtain the explicit solution of the unknown shrinkage strength.And then,a new estimator of covariance matrix,the cross-validation contraction estimator[CVS]is presented.The results show that when applied to a portfolio with a wide range of estimates,[CVS]estimators provide investors with higher returns and economic benefits.

关 键 词：协方差矩阵 交叉验证收缩估计量 投资组合 

分 类 号：O213[理学—概率论与数理统计]