  Recently many regularized estimators of large covariance matrices have been
proposed, and the tuning parameters in these estimators are usually selected
via cross-validation. However, there is no guideline on the number of folds for
conducting cross-validation and there is no comparison between cross-validation
and the methods based on bootstrap. Through extensive simulations, we suggest
10-fold cross-validation (nine-tenths for training and one-tenth for
validation) be appropriate when the estimation accuracy is measured in the
Frobenius norm, while 2-fold cross-validation (half for training and half for
validation) or reverse 3-fold cross-validation (one-third for training and
two-thirds for validation) be appropriate in the operator norm. We also suggest
the "optimal" cross-validation be more appropriate than the methods based on
bootstrap for both types of norm.
