Corrected Akaike information criterion

Index: The Book of Statistical Proofs ▷ Model Selection ▷ Classical information criteria ▷ Akaike information criterion ▷ Corrected AIC

Definition: Let $m$ be a generative model with likelihood function $p(y \vert \theta, m)$ and maximum likelihood estimates

\[\label{eq:MLE} \hat{\theta} = \operatorname*{arg\,max}_\theta \log p(y | \theta, m) \; .\]

Then, the corrected Akaike information criterion ($\mathrm{AIC}_\mathrm{c}$) of this model is defined as

\[\label{eq:AICc} \mathrm{AIC}_\mathrm{c}(m) = \mathrm{AIC}(m) + \frac{2k^2 + 2k}{n-k-1}\]

where $\mathrm{AIC}(m)$ is the Akaike information criterion and $k$ is the number of free parameters estimated via \eqref{eq:MLE}.

Sources:

Hurvich CM, Tsai CL (1989): "Regression and time series model selection in small samples"; in: Biometrika, vol. 76, no. 2, pp. 297-307; URL: https://academic.oup.com/biomet/article-abstract/76/2/297/265326; DOI: 10.1093/biomet/76.2.297.

Metadata: ID: D171 | shortcut: aicc | author: JoramSoch | date: 2022-02-11, 06:49.