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Proof of AIC criterion

Discussion in 'Education' started by mohammad, Oct 8, 2018.

  1. mohammad

    mohammad Guest

    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 $230$)

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