Figure 1

The partition of a data set for model selection and the estimation of the cross-validation error and prediction error. In the inner loop cross-validation, inner training set and inner validation set are used to determine the number of principal components (PC), and the model is fit on the inner training set. In the outer loop cross-validation, the model is built on the inner training set and the inner validation set, and an outer validation set are used to estimate the cross- validation error. In prediction, the model is built on the inner training set and the inner validation set, and the test set is used to obtain the prediction error.