Model selection in GLM based on the distribution function criterion

Abstract

In this article, we propose a model selection criterion based on the cumulative distribution function (CDF) of response variable called distribution function based criterion (DFC). The DFC is obtained by penalizing the scaled squared difference between CDFs of candidate model and full model. Under certain weak conditions, DFC is shown to be a consistent model selection criterion. We also discuss the use of DFC for link function selection. An extensive simulation study is performed to compare the performance of DFC with the existing methods.