Modified AIC and MDL model selection criteria for short data records

The classical model selection rules such as Akaike information criterion (AIC) and minimum description length (MDL) have been derived assuming that the number of samples (measurements) is much larger than the number of estimated model parameters. For short data records, AIC and MDL have the tendency to select overly complex models. This paper proposes modified AIC and MDL rules with improved finite sample behavior. They are useful in those measurement applications where gathering a sample is very time consuming and/or expensive.