Tweedie\u27s Compound Poisson Model with Grouped Elastic Net

Tweedie\u27s Compound Poisson model is a popular method to model data with probability mass at zero and non-negative, 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 re-weighted least square strategy. In together 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 onlin