Generally, is it useful to carry out statistical calibration tests on purely predictive models? For instance, if I build predictive model and I choose final model relying on cross validation results (Akaike, AUC, etc.), what additional info can the Hosmer-Lemeshow test give me? Assuming that I don't care about interpretation of model parameters, my only goal is the highest possible result on validation and test sets. My problem is that I have a small amount of training and testing data, but I want a model that generalizes well to real world.
To narrow the question: Can the results of Hosmer-Lemeshow tests be used to compare predictive models? Is it reasonable thing to do?