Statistical Fitting Criterion on the Basis of Cross-Validation Estimation

The statistical properties of cross-validation estimation as a criterion for choosing a decision model (a method for generating the decision function) are studied in the paper. For the variance analysis problem it is proved that the cross-validation criterion is equivalent to Fisher’s criterion for testing a homogeneity hypothesis under a certain significance level. It is revealed that the cross-validation criterion used for choosing the decision function among a certain one-parameter class and optimal decision function generation in the framework of a Bayesian model with normal parameter distribution are the same.