Empiricising Akaike's Information Criterion

We demonstrate that Owen's concept of empirical likelihood can be combined with Akaike's extension of the maximum likelihood principle to obtain an empirical analogue of Akaike's Information Criterion (AIC). We call this analogue the Empirical Information Criterion (EIC), and show that it is asymptotically an unbiased estimate of the same quantity that AIC estimates. A simulation study in the context of polynomial regression indicates good agreement between AIC and EIC in finite samples.