基于网络结构的高维协方差矩阵估计

High-Dimensional Covariance Matrix Estimation Based on Network

本文在Lan等[1]利用网络结构对连续变量协方差矩阵进行估计的研究基础上进行改进和扩展,给出一种基于网络结构的高维协方差矩阵估计方法,并允许响应变量异方差性存在.该方法将高维协方差矩阵的估计问题转化为关于网络结构的低维线性回归的参数估计问题,从而极大减少了计算量.在有限样本甚至n=1的情况下,该估计方法仍然适用,且估计效果会随着矩阵维数的增大而提高.此外,本文给出一种利用协方差矩阵识别网络中关键节点的方法,该方法能同时兼顾节点自身的贡献和节点对其他节点的影响程度,因此十分适用于学术合作网络.

A new method for estimating high-dimensional covariance matrix based on network structure with heteroscedasticity of response variables is proposed in this paper.This method greatly reduces the computational complexity by transforming the high-dimensional covariance matrix estimation problem into a low-dimensional linear regression problem.Even if the size of sample is finite,the estimation method is still effective.The error of estimation will decrease with the increase of matrix dimension.In addition,this paper presents a method of identifying influential nodes in network via covariance matrix.This method is very suitable for academic cooperation networks by taking into account both the contribution of the node itself and the impact of the node on other nodes.