I am confused about the concept of cross validation and its usage.
As I read about cross validation before, it is a way of validating a model. I did cross validation in my project (developing different regression models on a dataset, model validation and finally choosing best model). Cross validation just give me a model but no statistical criteria that shows ability of the model. By the way each time that I run cross validation (in R program) the result is different because train dataset is changed. For selecting the best model, I calculate AIC for the model obtained by cross validation but now I think it is wrong. Because first, train data used for each model is different, and second, even for a certain model, AIC will change by repeating cross validation.
Lately I read that cross validation is used for selecting the best model! All these confused me about utility of cross validation and the way of interpreting the result.
Could you please help me on figuring out all these?