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Akaike information criterion

{c}

For a full-rank $n\times p$ <normal linear model> with error variance $\sigma^2$, the maximum-likelihood residual variance satisfies
$$
\widehat\sigma^2\overset d=\frac{\sigma^2}{n}\chi^2_{n-p}.
$$
Consequently
$$
\operatorname{AIC}\overset d=
n\log(\chi^2_{n-p})+n\bigl(\log(2\pi\sigma^2/n)+1\bigr)+2(p+1).
$$

Distribution of the Akaike information criterion in a normal linear model

Past exam of the mathematics course of the University of Cambridge / 2020 / ii / Paper 3 / 5J / c / Solution

Distribution of the Akaike information criterion in a normal linear model

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Distribution of the Akaike information criterion in a normal linear model

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