Estimation of Covariance Matrices

Abstract

This article introduces covariance regression analysis for a p-dimensional response vector. The proposed method explores the regression relationship between the p-dimensional covariance matrix and auxiliary information. We study two types of estimators: maximum likelihood and ordinary least squares (OLS). Then, we demonstrate that these regression estimators are consistent and asymptotically normal. Furthermore, we obtain the high dimensional and large sample properties of the corresponding covariance matrix estimators. Simulation experiments are presented to demonstrate the performance of both regression and covariance matrix estimates. An example is analysed from the Gross Domestic Product (GDP) to illustrate the usefulness of the proposed covariance regression model.