SURE-tuned tapering estimation of large covariance matrices

Bandable covariance matrices are often used to model the dependence structure of variables that follow a nature order. It has been shown that the tapering covariance estimator attains the optimal minimax rates of convergence for estimating large bandable covariance matrices. The estimation risk critically depends on the choice of the tapering parameter. We develop a Stein’s Unbiased Risk Estimation (SURE) theory for estimating the Frobenius risk of the tapering estimator. SURE tuning selects the minimizer of SURE curve as the chosen tapering parameter. An extensive Monte Carlo study shows that SURE tuning is often comparable to the oracle tuning and outperforms cross-validation. We further illustrate SURE tuning using rock sonar spectrum data. The real data analysis results are consistent with simulation findings.