Testing the model selection in regression analysis with the Del distribution

This paper proposes a new Del distribution and discusses its applications in the model selection. The authors attempted to propose the exact distribution Del, which is defined as the difference between two generalized information criteria (GIC) of the ith and jth fitted models, and identified the relationship of Del with Correlated F-Ratio. Moreover, the density function and moments of the Del distribution were derived, and the critical points were also computed for different sample sizes at 5% and 1% significance levels. Finally, the application of the proposed distribution was used to scrutinise the equality between the pair of fitted candidate models. If the Del is said to be statistically significant, then the information loss between the models is not equal, and the predictive power of the models is not the same. This was numerically illustrated by fitting four different types of stepwise regression models based on 30 independent variables belonging to macroeconomic factors.