We consider the mean prediction error of a classification or regression procedure as well as
its cross-validation estimates, and investigate the variance of this estimate as a function of …

We consider choosing an estimator or model from a given class by cross validation
consisting of holding a nonneglible fraction of the observations out as a test set. We derive …

Cross-validation is a widely used technique to estimate prediction error, but its behavior is
complex and not fully understood. Ideally, one would like to think that cross-validation …

Cross validation is widely used to assess the performance of prediction models for unseen
data. Leave-k-out and m-fold are among the most popular cross validation criteria, which …

Cross validation is a central tool in evaluating the performance of machine learning and
statistical models. However, despite its ubiquitous role, its theoretical properties are still not …

An important question in cross-validation (CV) is whether rules can be established to allow
optimal sample size selection of the training/test set, for fixed values of the total sample size …

An important question in constructing Cross Validation (CV) estimators of the generalization
error is whether rules can be established that allow" optimal" selection of the size of the …

Theoretical developments on cross validation (CV) have mainly focused on selecting one
among a list of finite-dimensional models (eg, subset or order selection in linear regression) …

This text is a survey on cross-validation. We define all classical cross-validation procedures,
and we study their properties for two different goals: estimating the risk of a given estimator …

K-fold cross-validation produces variable estimates, whose variance cannot be estimated
unbiasedly. However, in practice, one would like to provide a figure related to the variability …