The banding estimator of Bickel and Levina (2008a) and its tapering version of Cai, Zhang and Zhou (2010) are important high dimensional covariance estimators. Both estimators require a band width parameter. We propose a band width 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 band width selector is established.  We provide a lower bound for  the coverage probability of  the underlying  band width being contained in an interval around the band width estimate.  Extensions to the band width 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.