Past exam of the mathematics course of the University of Cambridge / 2022 / iii / Paper 218 / 5 / c / ii

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- Solution ii

Solution

At the maximum-likelihood estimates,

σ_{1}^{2} = \frac{1}{n} ∥ Y - X β ∥_{2}^{2},

so

- 2 ℓ (β, σ_{1}^{2}) = n {lo g (2 π σ_{1}^{2}) + 1} .

There are

p

regression coefficients and one variance parameter. Adding twice this parameter count gives

AIC (M_{1}) = n {lo g (2 π σ_{1}^{2}) + 1} + 2 (p + 1) .

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