I'm considering using the AICc instead of the AIC to select models because my sample size is not much larger than my number of parameters (n=214, K=16 - which is not enough, according to Burnham and Anderson page 66).
However, whilst they don't really say much as to the assumptions we need to make in their book, wikipedia seem to indicate some of the assumptions we need to make on the model so that the formule for AICc holds:
I don't understand what
assuming that the model is univariate mean. I'm doing variable selection, across 16 variables (I plan on fixing many of them, because otherwise I'll just have overfitting) and I know that my model is not univariate. Otherwise I would just compare the 16 models with one variable.
Furthermore, I'm not sure how I can verify the other assumptions (them being:
Assuming that the model [...] is linear in its parameters, and has normally-distributed residuals (conditional upon regressors)).