The Annals of Statistics

Model Selection Via Multifold Cross Validation

Ping Zhang

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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.

Article information

Ann. Statist., Volume 21, Number 1 (1993), 299-313.

First available in Project Euclid: 12 April 2007

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


Primary: 62J05: Linear regression
Secondary: 62E20: Asymptotic distribution theory 65C05: Monte Carlo methods

Bootstrap FPE criterion model selection multifold cross validation


Zhang, Ping. Model Selection Via Multifold Cross Validation. Ann. Statist. 21 (1993), no. 1, 299--313. doi:10.1214/aos/1176349027.

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