Selection Consistency of EBIC for GLIM with Non-canonical Links and Diverging Number of Parameters

In this article, we investigate the properties of the EBIC in variable selection for generalized linear models with non-canonical links and diverging number of parameters in ultra-high dimensional feature space. The selection consistency of the EBIC in this situation is established under moderate conditions. The finite sample performance of the EBIC coupled with a forward selection procedure is demonstrated through simulation studies and a real data analysis.