A Best Linear Empirical Bayes Method for High-Dimensional Covariance Matrix Estimation

Covariance matrix estimation plays a significant role in both the theory and practice of portfolio analysis risk management. This paper deals with available data prior to developing factor model enhance covariance estimation. Our work has two main outcomes. First, for general linear unknown parameters, class best empirical Bayes estimators is established through kinds architectures improve accuracy by utilizing additional prior. The theoretical results indicate key points: proposed are equivalent minimum mean-square error estimator when complete or sufficient partial provided; perform better than optimal weighted least squares method, which ignores each situation. Second, used calculating high-dimensional models. numerical example simulation verify effectiveness our methods.