A robust generalization and asymptotic properties of the model selection criterion family

ABSTRACT

When selecting a model, robustness is a desirable property. However, most model selection criteria that are based on the Kullback–Leibler divergence tend to have reduced performance when the data are contaminated by outliers. In this paper, we derive and investigate a family of criteria that generalize the Akaike information criterion (AIC). When applied to a polynomial regression model, in the non contaminated case, the performance of this family of criteria is asymptotically equal to that of the AIC. Moreover, the proposed criteria tend to maintain sufficient levels of performance even in the presence of outliers.

KEYWORDS:

• BHHJ divergence
• model selection
• nonhomogeneous data
• polynomial regression
• 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.

Funding

This work was partly supported by JSPS KAKENHI [grant number 16J04579].