AIC in the well-specified linear model: theory and simulation

Theory

AIC

Consider the AIC for the usual linear model \(Y = X\beta + \varepsilon\):

\[

\text{AIC} = \frac{1}{2}\ln(2\pi e\hat \sigma^2)+\frac{p+1}{N}

(\#eq:AIC)

\]

where \(p\) is the dimension of the

covariate vector \(X\) and \(\hat \sigma ^2\) is...

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