Covariance Matrix Estimation Via Network Structure

35 Pages Posted: 20 Mar 2016

See all articles by Wei Lan

Wei Lan

Peking University - Guanghua School of Management

Zheng Fang

Sichuan University - Business School

Hansheng Wang

Peking University - Guanghua School of Management

Chih-Ling Tsai

University of California, Davis - Graduate School of Management

Date Written: March 19, 2016

Abstract

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

Lan, Wei and Fang, Zheng and Wang, Hansheng and Tsai, Chih-Ling, Covariance Matrix Estimation Via Network Structure (March 19, 2016). Available at SSRN: https://ssrn.com/abstract=2750348 or http://dx.doi.org/10.2139/ssrn.2750348

Wei Lan

Peking University - Guanghua School of Management ( email )

Peking University
Beijing, Beijing 100871
China

Zheng Fang

Sichuan University - Business School ( email )

China

Hansheng Wang (Contact Author)

Peking University - Guanghua School of Management ( email )

Peking University
Beijing, Beijing 100871
China

HOME PAGE: http://hansheng.gsm.pku.edu.cn

Chih-Ling Tsai

University of California, Davis - Graduate School of Management ( email )

One Shields Avenue
Davis, CA 95616
United States

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