On the consistency and the robustness in model selection criteria

Abstract

In the model selection problem, the consistency of the selection criterion has been often discussed. This paper derives a family of criteria based on a robust statistical divergence family by using a generalized Bayesian procedure. The proposed family can achieve both consistency and robustness at the same time since it has good performance with respect to contamination by outliers under appropriate circumstances. We show the selection accuracy of the proposed criterion family compared with the conventional methods through numerical experiments.

Keywords:

• Model selection
• BHHJ divergence
• influence function
• consistency
• robustness

Acknowledgments

The authors would like to express their gratitude to the reviewer and the editor in chief for their valuable comments, which have considerably improved the earlier version of the article.

Additional information

Funding

This work was partly supported by JSPS KAKENHI Grant Number 16J04579 and 18K03413.