Cross-validation for estimator selection

Cross-validation is a widespread strategy because of its simplicity and its (apparent) universality. 
It can be used with two main goals: 
(i) estimating the risk of an estimator, and 
(ii) model selection or hyperparameter tuning, or more generally for choosing among a family of estimators. 
Many results exist on the performance of cross-validation procedures, which can strongly depend on the goal for which it is used. 

This talk will show the big picture of these results, with an emphasis on the goal of estimator selection. 
In short, at first order (when the sample size goes to infinity), the key parameter is the bias of cross-validation, which only depends on the size of the training set. 
Nevertheless, "second-order" terms do matter in practice, and I will show recent results on the role of the "variance" of cross-validation procedures on their performance. 
As a conclusion, I will provide some guidelines for choosing the best cross-validation procedure according to the particular features of the problem at hand. 

References: 
	Survey paper (with Alain Celisse): http://projecteuclid.org/euclid.ssu/1268143839
	Preprint on V-fold cross-validation (role of the variance and choice of V, with Matthieu Lerasle): http://arxiv.org/abs/1210.5830