Model selection criterion produces non-normal residuals I was wondering if I can use Akaike or Schwarz criterion even when the residuals that I get from the model when I run the regression are not normal.  Is there any normality assumption with these criteria or can I use them all the time regardless?
 A: We use the Akaike or Schwarz information criteria to compare a set of "Candidate Models". The candidates means that you have already fitted your regression models and did the model adequacy checking including the normality assumption of your residuals. You are just not sure about the balance between the number of parameters used to fit the model and the closeness of the fit. Even though you may not see a direct normality assumption in the definitions of AIC or BIC criteria, but (as far as I can say) you need to check the normality assumption before comparing your models. Of course, you can still apply these criteria, even for non-normal errors. But how meaningful would be you final model, will be under a big question mark. You can also have a look at this question.
A: AIC and BIC both have consist of two elements: the likelihood and the penalty for the number of parameters. The likelihood need not be normal likelihood, it can be whatever you find reasonable. 
However, if you assume the likelihood to be normal (and use it in AIC or BIC), you need normal residuals, too. In other words, the distribution of residuals has to match the distributional assumption used to calculate the likelihood for AIC or BIC. 
