How do the models differ? If model A describes the relationship between X and Y as linear, whereas model B describes the relationship with a n-degree polynomial, and on top of that, both models contain the same (or no other) parameters, then B is nested in A and you should be able to use model comparison.

Many thanks for your reply. Model A is a gaussian model of the form a1*exp(-((x-b1)/c1)^2) + ... + aN*exp(-((x-bN)/cN)^2) model B is a n-degree polynomial so they do not have the same number of parameters, hence they both do not describe a linear relationship (and they should not as the data is mostly not linear). The question is whether the validity of the two models can be compared just with cross validation or if a criteria like AIC is also needed to demonstrate the optimality of the fit. Hope this clarifies my question

I developed the 100-fold cross-validation for small sample method. It can offer the 95% confidence interval of discriminant coefficients and error rate. Moreover, the best model with minimum mean error rate in the validation samples. It is very simple and powerful model selection. I compare my methods with LOO, AIC, BIC and Cp statistics using over ten data. My research is the discrimination. However, my method is usuful for regression analysis and other methods. See my papers onRG.