On Cross Validation for Model Selection

In response to Zhu and Rower (1996), a recent communication (Goutte, 1997) established that leave-one-out cross validation is not subject to the “no-free-lunch” criticism. Despite this optimistic conclusion, we show here that cross validation has very poor performances for the selection of linear models as compared to classic statistical tests. We conclude that the statistical tests are preferable to cross validation for linear as well as for nonlinear model selection.