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.
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- Rothman, Adam J. & Levina, Elizaveta & Zhu, Ji, 2009. "Generalized Thresholding of Large Covariance Matrices," Journal of the American Statistical Association, American Statistical Association, vol. 104(485), pages 177-186.
- Adam J. Rothman & Elizaveta Levina & Ji Zhu, 2010. "A new approach to Cholesky-based covariance regularization in high dimensions," Biometrika, Biometrika Trust, vol. 97(3), pages 539-550.
- Bradley Efron, 2004. "The Estimation of Prediction Error: Covariance Penalties and Cross-Validation," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 619-632, January.
- Furrer, Reinhard & Bengtsson, Thomas, 2007. "Estimation of high-dimensional prior and posterior covariance matrices in Kalman filter variants," Journal of Multivariate Analysis, Elsevier, vol. 98(2), pages 227-255, February.
- Jianhua Z. Huang & Naiping Liu & Mohsen Pourahmadi & Linxu Liu, 2006. "Covariance matrix selection and estimation via penalised normal likelihood," Biometrika, Biometrika Trust, vol. 93(1), pages 85-98, March.
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