A simple application of FIC to model selection
This provides an incremental demonstration of FIC for model selection in statistics, with limited practical impact.
The paper tackles model selection by applying the Frequentist Information Criterion (FIC) to a simplified example, demonstrating that it naturally yields model complexities scaling like AIC (N^0) and BIC (log N) with observation number N.
We have recently proposed a new information-based approach to model selection, the Frequentist Information Criterion (FIC), that reconciles information-based and frequentist inference. The purpose of this current paper is to provide a simple example of the application of this criterion and a demonstration of the natural emergence of model complexities with both AIC-like ($N^0$) and BIC-like ($\log N$) scaling with observation number $N$. The application developed is deliberately simplified to make the analysis analytically tractable.