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. In this article, we propose a distribution function based criterion (DFC) which penalizes the squared difference between distribution function of the response variable based on the candidate and the full model by the complexity of the model via the number of predictors in the model. Distribution function is familiar to investigators and can be computed using any statistical software. Moreover, DFC is computationally simpler as compared to existing model selection criteria. Under certain weak conditions, minimizing DFC results in consistent model selection in the sense that with probability approachingto one model selected is asymptotically equal to the optimal model which contains