Improved Shrinkage Estimators of Covariance Matrices With Toeplitz-Structured Targets in Small Sample Scenarios

Shrinkage regularization is an effective strategy to estimate the covariance matrix of multi-variate random vector in small sample scenarios. The purpose of this paper is to propose improved linear shrinkage estimators of covariance matrix as two types of Toeplitz-structured target matrices are respectively employed in the shrinkage procedure. Under Gaussian and non-Gaussian distributions, the corresponding shrinkage estimators are respectively obtained in closed form by unbiasedly estimating the unknown scalar quantities which involve the true covariance matrix. Compared with the existing estimators of same type, the proposed covariance estimators show a significant improvement on the mean squared error in numerical simulations. Moreover, example applications including portfolio risk estimation and classification of real data are provided for verifying the performance of proposed covariance estimators in small sample scenarios.