Tweedie’s Compound Poisson Model With Grouped Elastic Net

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.

特威迪复合泊松模型（Tweedie’s compound Poisson model）是一类用于建模存在零概率质量、非负且高度右偏分布数据的常用方法。鉴于该模型在精算科学等诸多领域的广泛应用，本文在广义线性模型（generalized linear model）框架下，针对特威迪复合泊松模型研究分组弹性网（grouped elastic net）方法。为高效求解估计系数，本文设计了一种双层算法，将分块优度下降法（blockwise majorization descent method）嵌入迭代重加权最小二乘策略中。结合强规则（strong rule），本文所提算法已在易用的R包HDtweedie中实现，并被证实可高效求解完整解路径。本文通过模拟实验，研究并对比了各类套索（lasso）方法针对特威迪复合泊松模型的变量选择与模型拟合性能。本文通过分析车险理赔数据集，展示了该模型在保险业务风险细分领域的建模应用场景。本文的补充材料可在线获取。