Cross-validation is a resampling method as well, similar to the jackknife. However, the aim is now not to make inference statistics but to estimate prediction errors.
Cross-validation is mainly used for the comparison of methods or to find the optimal values of parameters in an estimation model.
In the following section, we will explain cross-validation based on regression analysis. For readers who have never heard of regression analysis, we recommend to read a basic textbook about regression analysis. We only point out some very basic issues.
The classical linear regression model in its simplest case with one response and one predictor is given by with . In matrix notation, this is
, with the ...