Model Selection Via Multifold Cross Validation

A natural extension of the simple leave-one-out cross validation (CV) method is to allow the deletion of more than one observations. In this article, several notions of the multifold cross validation (MCV) method have been discussed. In the context of variable selection under a linear regression model, we show that the delete-d MCV criterion is asymptotically equivalent to the well known FPE criterion. Two computationally more feasible methods, the r-fold cross validation and the repeated learning-testing criterion, are also studied. The performance of these criteria are compared with the simple leave-one-out cross validation method. Simulation results are obtained to gain some understanding on the small sample properties of these methods.