2013/08/15 by Yixin Fang, Fang, Yixin, Binhuan Wang +3
Mathematics · #Computation (stat.CO) #FOS: Computer and information sciences #Methodology (stat.ME) #stat.CO #stat.ME
paper · pdf · doi:10.48550/arxiv.1308.3416
arxiv created 2013/08/15 · arxiv updated 2013/08/16
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.