Statistics Surveys

A survey of cross-validation procedures for model selection

Sylvain Arlot and Alain Celisse

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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.

Article information

Statist. Surv., Volume 4 (2010), 40-79.

First available in Project Euclid: 9 March 2010

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62G08: Nonparametric regression
Secondary: 62G05: Estimation 62G09: Resampling methods

Model selection cross-validation leave-one-out


Arlot, Sylvain; Celisse, Alain. A survey of cross-validation procedures for model selection. Statist. Surv. 4 (2010), 40--79. doi:10.1214/09-SS054.

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