Proof of AIC criterion

by mohammad   Last Updated October 08, 2018 20:19 PM

I was recently read the book "Elements Of Statistical Learning" by Hastie 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 $230$)

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