I was recently read the book "Elements Of Statistical Learning" by Hastie et.al. In chapter $7$, AIC criterion is definite as follows: $$-2.E[log Pr_\hat\theta(Y)]\approx -\frac{2}{N}.E[loglik]+2\frac{d}{N}$$ that loglik is: $$loglik=\sum_{i=0}^Nlog Pr_\hat\theta(y_i)$$ but proof of this equation is not available in this book. I search about this equation but I can't find anything to understand it. can any one proof it in understandable way? (equation $(7.27)$ on page $230$) Login To add answer/comment