Group regularization for zero-inflated poisson regression models with an application to insurance ratemaking

ABSTRACT

Zero-inflated count models have received considerable amount of attention in recent years, fuelled by their widespread applications in many scientific disciplines. In this paper, we consider the problem of selecting grouped variables in zero-inflated Poisson (ZIP) models via group bridge regularization. The ZIP mixture likelihood with a group-wise $L_1$ penalty on the coefficients is formulated using least squares approximation and then the parameters involved in the penalized likelihood are estimated by an efficient group descent algorithm. We examine the effectiveness of our modeling procedure through extensive Monte Carlo simulations. An auto insurance claim dataset from the SAS Enterprise Miner database is analyzed for illustrative purposes. Finally, we derive theoretical properties of the proposed group variable selection procedure under certain regularity conditions. The open source software implementation of this method is publicly available at https://github.com/himelmallick/Gooogle.

KEYWORDS:

• Zero-inflated poisson
• group regularization
• bi-level variable selection
• LASSO
• group bridge
• ratemaking

Acknowledgments

The authors would like to thank the anonymous reviewers for their valuable comments and suggestions to improve the manuscript. This work was supported in part by the research computing resources acquired and managed by University of Alabama at Birmingham IT Research Computing. Any opinions, findings and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the University of Alabama at Birmingham.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Shrabanti Chowdhury  http://orcid.org/0000-0001-8429-7822

Himel Mallick  http://orcid.org/0000-0003-4956-2429