Past exam of the mathematics course of the University of Cambridge / 2023 / iii / Paper 218 / 3 / c

For a likelihood $L(\theta )$ with $k$ estimated parameters, the Akaike information criterion iswhere $\hat{\theta }$ is the maximum-likelihood estimator. Among likelihoods for the same observed response and reference measure, smaller AIC estimates smaller expected out-of-sample Kullback-Leibler divergence up to a model-independent constant.