Covariance Matrix Estimation Via Network Structure
35 Pages Posted: 20 Mar 2016
Date Written: March 19, 2016
In this article, we employ a regression formulation to estimate the high dimensional covariance matrix for a given network structure. Using prior information contained in the network relationships, we model the covariance as a polynomial function of the symmetric adjacency matrix. Accordingly, the problem of estimating a high dimensional covariance matrix is converted to one of estimating low dimensional coeﬃcients of the polynomial regression function, which we can accomplish using ordinary least squares or maximum likelihood. The resulting covariance matrix estimator based on the maximum likelihood approach is guaranteed to be positive deﬁnite even in ﬁnite samples. Under mild conditions, we obtain the theoretical properties of the resulting estimators. A Bayesian information criterion is also developed to select the order of the polynomial function. Simulation studies and empirical examples illustrate the usefulness of the proposed methods.
Keywords: Adjacency Matrix; Bayesian Information Criterion; Covariance Estimation; Covariance Regression Network Model; High Dimensional Data
JEL Classification: C3
Suggested Citation: Suggested Citation