\(\hat{Err}_{in} = \overline{err} + \hat{w}\). If squared error loss, we obtain \(C_p = \overline{err} + 2 \frac{d}{N} \hat{\sigma}^2_\varepsilon\). Use MSE of a low-bias model for \(\hat{\sigma}^2_\varepsilon\).
If log-likelihood loss, another estimate of $Err_{in}$ is \(AIC = \frac{2}{N} (- logik + d)\). For Gaussian model, AIC is equivalent to $C_p$.
If $d$ basis functions are chosen adaptively from $p$ inputs, effective number of parameters is more than $d$.
For nonlinear models, replace $d$ with some measure of model complexity.
TODO: (7.30) formulation of AIC.