A Novel Consistent Information Criterion for Model Selection Based on Empirical Likelihood

• Activity Number: 499 - Section on Nonparametric Statistics - Student Paper Competition Presentations
• Type: Topic Contributed
• Date/Time: Wednesday, July 31, 2019 : 10:30 AM to 12:20 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Chixiang Chen* and Ming Wang and Rongling Wu and Runze Li
• Companies: Pennsylvania State University and Pennsylvania State University and Pennsylvania State University and Penn State University
• Keywords: Empirical likelihood; Model selection; Generalized estimating equations; Generalized linear models; Penalized regressions

Abstract

Conventional likelihood-based information criteria for model selection rely on the distribution assumption of data, which has proven to be challenging and not suitable for all model selection problems, such as correlation structure selection under discrete outcomes. Here, we propose a robust and consistent model selection criterion framework under which the distribution part is data-driven via empirical likelihood. In particular, our framework is derived from the asymptotic expansion of marginal distribution based on the empirical likelihood, where the estimation is relaxed by solving external estimating equations, not limited to empirical likelihood. Importantly, such a framework implemented with plug-in estimators is versatile, allowing model selection to be performed under a wide range of contexts. We further establish the consistency property of this framework under mild conditions. Results from simulation studies show that our model selection framework performs better in many cases, compared with classical model selection criteria. Finally, this proposed framework is validated by a real data application from the Atherosclerosis Risk in Communities Study.