Maximum Likelihood Criterion for Non-nested Model Selection

2026-06-21

AI Summary

This work addresses the failure of traditional penalized methods in non-nested model selection by proposing a maximum likelihood-based criterion that selects the model with the highest likelihood without favoring simpler models or relying on explicit penalties for model complexity. Under the assumption that all candidate models are equally important a priori, the method directly chooses the model maximizing the likelihood and is theoretically shown to be statistically consistent. Both theoretical analysis and empirical experiments demonstrate that the proposed criterion not only achieves consistency in non-nested settings but also outperforms existing penalized model selection approaches in terms of selection accuracy and overall performance.

Abstract

Penalization is a widely used approach to model selection with roots in information theory and Bayesian inference. We study a model selection problem involving non-nested candidate models for which penalization is counterproductive. We propose a Maximum Likelihood Criterion for this non-nested setting that selects the candidate model with the highest maximum likelihood. This criterion does not take into consideration the number of parameters of a candidate model. It is well-suited for situations where all candidate models are regarded as equal with no preference for models having fewer parameters. We establish the consistency of this criterion and compare its performance with that of existing penalization-based criteria.

Problem

• non-nested model selection
• maximum likelihood
• model selection
• penalization
• parameter parsimony

Innovation

• Maximum Likelihood Criterion
• non-nested model selection
• penalization-free
• model consistency
• likelihood-based selection