Covariance Regression Analysis

This article introduces covariance regression analysis for a <i>p</i>-dimensional response vector. The proposed method explores the regression relationship between the <i>p</i>-dimensional covariance matrix and auxiliary information. We study three types of estimators: maximum likelihood, ordinary least squares, and feasible generalized least squares estimators. 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 analyzed from the Chinese stock market to illustrate the usefulness of the proposed covariance regression model. Supplementary materials for this article are available online.