Bandwidth Selection for High-Dimensional Covariance Matrix Estimation
Yumou Qiu and
Journal of the American Statistical Association, 2015, vol. 110, issue 511, 1160-1174
The banding estimator of Bickel and Levina and its tapering version of Cai, Zhang, and Zhou are important high-dimensional covariance estimators. Both estimators require a bandwidth parameter. We propose a bandwidth selector for the banding estimator by minimizing an empirical estimate of the expected squared Frobenius norms of the estimation error matrix. The ratio consistency of the bandwidth selector is established. We provide a lower bound for the coverage probability of the underlying bandwidth being contained in an interval around the bandwidth estimate. Extensions to the bandwidth selection for the tapering estimator and threshold level selection for the thresholding covariance estimator are made. Numerical simulations and a case study on sonar spectrum data are conducted to demonstrate the proposed approaches. Supplementary materials for this article are available online.
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Working Paper: Band Width Selection for High Dimensional Covariance Matrix Estimation (2014)
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