Model averaging estimation for high-dimensional covariance matrices with a network structure

Rong Zhu; Xinyu Zhang; Yanyuan Ma; Guohua Zou

doi:10.1093/ectj/utaa030

Model averaging estimation for high-dimensional covariance matrices with a network structure

Econom J. 2020 Sep 29;24(1):177-197. doi: 10.1093/ectj/utaa030. eCollection 2021 Jan.

Authors

Rong Zhu¹, Xinyu Zhang², Yanyuan Ma³, Guohua Zou⁴

Affiliations

¹ School of Mathematics, Statistics and Physics, Newcastle University, Newcastle upon Tyne NE1 7RU, UK.
² Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China.
³ Department of Statistics, Pennsylvania State University, University Park, PA 16802, USA.
⁴ School of Mathematical Sciences, Capital Normal University, Beijing 100048, China.

Abstract

In this paper, we develop a model averaging method to estimate a high-dimensional covariance matrix, where the candidate models are constructed by different orders of polynomial functions. We propose a Mallows-type model averaging criterion and select the weights by minimizing this criterion, which is an unbiased estimator of the expected in-sample squared error plus a constant. Then, we prove the asymptotic optimality of the resulting model average covariance estimators. Finally, we conduct numerical simulations and a case study on Chinese airport network structure data to demonstrate the usefulness of the proposed approaches.

Keywords: Mallows criterion; asymptotic optimality; consistency; covariance regression network model; model averaging.