标题： 空间 Tweedie 指数分散模型 显示英文标题

标题： Spatial Tweedie exponential dispersion models

摘要： 本文提出了一种通用的建模框架，允许在个体协变量层面进行不确定性量化和空间参考，在双广义线性模型（DGLM）内运行。 DGLMs 提供了一个通用的建模框架，允许离散度以链接线性方式依赖于选定的协变量。 我们专注于使用 Tweedie 指数离散模型，同时考虑 DGLMs，原因在于它们最近被广泛用于建模混合响应类型。 采用基于正则化的的方法，我们建议了一类从无向图导出的灵活凸惩罚，有助于估计未观察到的空间效应。 通过提出一个坐标下降算法，简明地展示了这些发展，该算法通过估计各自模型系数同时解释均值和离散度中的协变量变化，并估计未观察到的空间效应。 模拟结果显示，所提出的方法优于岭回归和未惩罚版本等竞争方法。 最后，考虑了一个实际数据应用，在美国康涅狄格州2008年汽车碰撞引起的保险损失建模中进行了分析。 显示英文摘要

摘要： This paper proposes a general modeling framework that allows for uncertainty quantification at the individual covariate level and spatial referencing, operating withing a double generalized linear model (DGLM). DGLMs provide a general modeling framework allowing dispersion to depend in a link-linear fashion on chosen covariates. We focus on working with Tweedie exponential dispersion models while considering DGLMs, the reason being their recent wide-spread use for modeling mixed response types. Adopting a regularization based approach, we suggest a class of flexible convex penalties derived from an un-directed graph that facilitates estimation of the unobserved spatial effect. Developments are concisely showcased by proposing a co-ordinate descent algorithm that jointly explains variation from covariates in mean and dispersion through estimation of respective model coefficients while estimating the unobserved spatial effect. Simulations performed show that proposed approach is superior to competitors like the ridge and un-penalized versions. Finally, a real data application is considered while modeling insurance losses arising from automobile collisions in the state of Connecticut, USA for the year 2008.