title: Risk factor selection in rate making: EM adaptive LASSO for zero-inflated poisson regression models.
abstract: Risk factor selection is very important in the insurance industry, which helps precise rate making and studying the features of high-quality insureds. Zero-inflated data are common in insurance, such as the claim frequency data, and zero-inflation makes the selection of risk factors quite difficult. In this article, we propose a new risk factor selection approach, EM adaptive LASSO, for a zero-inflated Poisson regression model, which combines the EM algorithm and adaptive LASSO penalty. Under some regularity conditions, we show that, with probability approaching 1, important factors are selected and the redundant factors are excluded. We investigate the finite sample performance of the proposed method through a simulation study and the analysis of car insurance data from SAS Enterprise Miner database.
authors.affiliation: Department of Mathematics, Tongji University, Shanghai, 200092, China.
authors.forename: Yanlin
authors.initials: Y
authors.lastname: Tang
authors.forename: Liya
authors.initials: L
authors.lastname: Xiang
authors.forename: Zhongyi
authors.initials: Z
authors.lastname: Zhu
mesh_terms: D000465:Algorithms; D016012:Poisson Distribution; D012044:Regression Analysis; D012307:Risk Factors
keywords: Adaptive LASSO; em algorithm; rate making; risk factor selection; zip regression model