半参数贝叶斯分层分位回归模型及其在保险公司成本分析中的应用  

A Semi-parametric Bayesian Hierarchical Quantile Regression Model and Its Application in Analysis of Insurance Company Costs

作　　者：张永霞[1,2] 孟生旺[1,2] 田茂再[1,2] ZHANG Yong-xia;MENG Sheng-wang;TIAN Mao-zai(Center for Applied Statistics,Renmin University of China,Beijing 100872,China;School of Statistics,Renmin University of China,Beijing 100872,China)

机构地区：[1]中国人民大学应用统计科学研究中心,北京100872 [2]中国人民大学统计学院,北京100872

出　　处：《数理统计与管理》2021年第3期381-394,共14页Journal of Applied Statistics and Management

基　　金：教育部人文社会科学重点研究基地重大项目(16JJD910001);国家社科基金重大项目(16ZDA052);中国博士后科学基金(2019M650928).

摘　　要：本文建立了一种半参数贝叶斯分层分位回归模型,并基于美国NAIC提供的多个保险公司连续多年期的非平衡纵向成本观测数据进行了实证分析.本文主要贡献包括三个方面:一是首次在有限正态混合误差假定下,对具有右偏厚尾性的成本数据建立半参数分层分位回归模型,并考虑到保险公司的聚类性,选用狄利克雷过程先验进行模型非参数部分的估计,进一步推广了分位回归模型在保险精算领域中的应用;二是通过模拟数据研究,系统比较了在非对称拉普拉斯误差假定下和有限正态混合误差假定下,半参数分层分位回归模型对复杂数据的拟合精度及参数估计的精确性,结果表明,有限正态混合误差更能充分捕捉数据的复杂性;三是通过实际观测的保险公司成本数据进行分析,选出了对成本具有较强效应的解释变量,并发现在不同分位数水平下各个解释变量对响应变量的效应具有较大区别.Based on the unbalanced longitudinal observation data of several insurance companies provided by the National Association of Insurance Commissioners(NAIC)for many years,this paper establishes a semiparametric Bayesian hierarchical quantile regression model for the cost of each insurance company.The main contributions of this paper include three aspects.First,for the first time,under the assumption of finite normal mixed error,the semi-parameter hierarchical quantile regression model is established for the cost data with right skewed and long tails,and considering the clustering nature of insurance companies,the Dirichlet process prior is used to estimate the parameters of the non-parametric part of the model.The application of the quantile regression model in the field of insurance is further promoted.Secondly,through simulation data research,the system compares the accuracy of fitting and accuracy of parameter estimation by semi-parametric hierarchical quantile regression model under the assumption of asymmetric Laplacian error and finite normal mixed error.The results show that the finite normal mixing error can fully capture the complexity of the data.Third,through the actual cost data analysis,the explanatory variables with strong effects on cost are selected,and it is found that the efFect of each explanatory variable on the response variable is different at different quantile levels.

关 键 词：分位回归 狄利克雷过程先验 单指标模型 贝叶斯参数估计 保险公司成本 

分 类 号：O212[理学—概率论与数理统计]