A survey of cross-validation procedures for model selection

Used to estimate the risk of an estimator or to perform model selection, cross-validation is a widespread strategy because of its simplicity and its (apparent) universality. Many results exist on model selection performances of cross-validation procedures. This survey intends to relate these results to the most recent advances of model selection theory, with a particular emphasis on distinguishing empirical statements from rigorous theoretical results. As a conclusion, guidelines are provided for choosing the best cross-validation procedure according to the particular features of the problem in hand.