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

TL;DR

This paper studies the selection consistency of the Extended Bayesian Information Criterion (EBIC) in high-dimensional generalized linear models with non-canonical links, establishing theoretical properties and demonstrating finite sample performance.

Contribution

It provides the first theoretical proof of EBIC's selection consistency in non-canonical GLIM with diverging parameters and validates its effectiveness through simulations and real data.

Findings

EBIC is consistent in high-dimensional non-canonical GLIM.

Forward selection with EBIC performs well in finite samples.

Simulation and real data confirm theoretical results.

Abstract

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.