On the Accuracy of Cross-Validation in the Classification Problem

In this work we will study the accuracy of the cross-validation estimates for decision functions. The main idea of the research consists in the scheme of statistical modeling that allows using real data to obtain statistical estimates, which are usually obtained only by using model (synthetic) distributions. The studies confirm the well-known empirical recommendation to choose the number of folds equal to 5 or more. The choice of more than 10 folds does not yield a significant increase in accuracy. The use of repeated cross-validation also does not provide fundamental gain in precision. The results of the experiments allow us to formulate an empirical fact that the accuracy of the estimates obtained by the cross-validation method is approximately the same as the accuracy of the estimates obtained from the test sample of half the size. This result can be easily explained by the fact that all the objects of the test sample are independent, and the estimates built by the cross-validation on different subsamples (folds) are not independent.