广义线性混合模型框架下的信度模型分析  

Credibility Analysis Based on Generalized Linear Mixed Models

作　　者：谢远涛[1] 王稳[1] 谭英平[1] 杨娟[2] 

机构地区：[1]对外经济贸易大学保险学院,北京100029 [2]中国人民大学统计学院,北京100872

出　　处：《统计与信息论坛》2012年第10期3-8,共6页Journal of Statistics and Information

基　　金：国家社科基金重点项目<风险管理与公司价值关系研究>(11AJY014);教育部人文社会科学青年基金项目<基于广义线性混合模型和信度的费率厘定研究>(10YJC790303);教育部人文社科基金规划项目<企业风险管理的分析框架及有效性研究>(10YJA790190)

摘　　要：尝试在广义线性混合模型的框架下构建信度模型。在广义线性混合模型框架中,假定被解释变量服从指数簇分布,假定自然参数先验分布为相应的自然共轭先验分布簇,按照Bayes理论,通过特殊构造,给出推论:对随机效应的估计满足经典信度公式。参数估计部分,利用自然共轭先验分布簇参数子列上下极限的性质找出先验分布参数的含义和关系,使用伪似然方法给出信度估计公式。并以特例形式讨论Tweedie模型,对模型进行变形,得到特例的Bühlmann-Straub信度和经典的Bühlmann信度。该模型同时考虑先验信息与后验信息,对整合分类费率与个体经验费率提供一定参考。This article try to construct a credibility model based on generalized linear mixed models.Suppose dependent variable follows exponential distribution family,natural parameters follows natural conjugate prior.This article introduces credibility factor into generalized linear mixed models to build a model with both priority information and posterior information included according to Bayesian theory,and concludes that the estimate of random effect coincide with the credibility formula.This article finds out the relationship between prior parameters by way of the limit of natural conjugate prior.Estimation can be achieved by way of pseudo-likelihood method.Bühlmann-Straub credibility and Bühlmann credibility can be treated as a special case of this model by transforming the Tweedie models which is discussed in this paper.This paper may contribute to rate making and credibility.

关 键 词：广义线性混合模型 广义线性模型 随机效应 信度模型 Bühlmann信度 B-S信度 

分 类 号：O212[理学—概率论与数理统计]