Tweedie’s Compound Poisson Model With Grouped Elastic Net

Wei Qian, Yi Yang & Hui ZouWei Qian is Assistant Professor, School of Mathematical Sciences, Rochester Institute of Technology, Rochester, NY 14623 (E-mail: wxqsma@rit.edu). Yi Yang is Assistant Professor, Department of Mathematics and Statistics, McGill University, Canada (E-mail: yi.yang6@mcgill.ca) Hui Zou is Professor of Statistics, School of Statistics, University of Minnesota, Minneapolis, MN 55455 (E-mail: zouxx019@umn.edu).Tweedie’s compound Poisson model is a popular method to model data with probability mass at zero and nonnegative, highly right-skewed distribution. Motivated by wide applications of the Tweedie model in various fields such as actuarial science, we investigate the grouped elastic net method for the Tweedie model in the context of the generalized linear model. To efficiently compute the estimation coefficients, we devise a two-layer algorithm that embeds the blockwise majorization descent method into an iteratively reweighted least square strategy. Integrated with the strong rule, the proposed algorithm is implemented in an easy-to-use R package HDtweedie, and is shown to compute the whole solution path very efficiently. Simulations are conducted to study the variable selection and model fitting performance of various lasso methods for the Tweedie model. The modeling applications in risk segmentation of insurance business are illustrated by analysis of an auto insurance claim dataset. Supplementary materials for this article are available online.