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Model selection via multifold cross validation. (English) Zbl 0770.62053

Summary: A natural extension of the simple leave-one-out cross validation (CV) method is to allow the deletion of more than one observation. 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.

MSC:

62J05 Linear regression; mixed models
62E20 Asymptotic distribution theory in statistics
65C05 Monte Carlo methods
62G20 Asymptotic properties of nonparametric inference
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