Covariance Regression Analysis
针对p维响应向量，提出协方差回归方法，研究协方差矩阵与辅助信息间的回归关系，给出三种估计量并证明其一致性和渐近正态性，通过模拟和中国股市数据验证模型有效性。
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 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.