Some Comments on Cross-Validation

Summary

A new variant of cross-validation, called full cross-validation, is proposed in order to overcome some disadvantages of the traditional cross-validation approach in general regression situations. Both criteria may be regarded as estimates of the mean squared error of prediction. Under some assumptions including normally distributed observations, the cross-validation criterion is shown to be outperformed by the full cross-validation criterion. Analogous modifications may be applied to the generalized cross-validation method, providing a similar improvement. This leads to the recommendation of replacing the traditional cross-validation techniques by the new ones for estimating the prediction quality of models or of regression function estimators.