High-dimensional covariance matrix regularization using informative targets

Abstract: The sample covariance matrix becomes non-invertible in high-dimensional settings, making classical multivariate statistical methods inapplicable. Various regularization techniques address this issue by imposing a structured target matrix to improve stability and invertibility. While diagonal matrices are commonly used as targets due to their simplicity, more informative target matrices can enhance performance. This paper explores the use of such targets and estimates the underlying correlation parameter using maximum likelihood. The proposed method is analytically straightforward, computationally efficient, and more accurate than recent regularization techniques when targets are correctly specified. Its effectiveness is demonstrated through extensive simulations and a real-world application.