Abstract
In this paper, an improved shrinkage-to-tapering oracle approximating approach for estimating high-dimensional covariance matrices is proposed. Since the oracle shrinkage coefficient of shrinkage-to-tapering oracle (STO) estimator is greater than one for some tapering parameter, the optimal shrinkage coefficient is obtained by thresholding the oracle coefficients. The corresponding normalized mean-squared error (MSE) is also obtained. Moreover, an improved shrinkage-to-tapering estimator is proposed by plugging the unbiased and consistent estimators of some functions of unknown covariance matrix into the optimal coefficient and corresponding normalized MSE. Compared with the STO approximating approach using iteration to approximate the oracle coefficient, a closed-form formula of the estimated coefficient and the normalized MSE are derived for given tapering parameter. Numerical simulations and an application to adaptive beamforming show the comparable performance of the proposed estimator.
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