基于贝叶斯的部分线性单指标复合分位回归的研究及其应用  

Research and Application of Partial Linear Single Index Composite Quantile Regression Based on Bayesian

作　　者：张永霞[1] 田茂再[1,2] ZHANG Yongxia;TIAN Maozai(Center for Applied Statistics,School of Statistics,Renmin University of China,Beijing 100872;College of Medical Engineering and Technology,Xinjiang Medical University,Urumqi 830011)

机构地区：[1]中国人民大学应用统计科学研究中心,中国人民大学统计学院,北京100872 [2]新疆医科大学医学工程技术学院,乌鲁木齐830011

出　　处：《系统科学与数学》2021年第5期1381-1399,共19页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金项目(11861042);中国博士后科学基金项目(2019M650928);全国统计科学研究项目重点项目(2020LZ25)资助课题。

摘　　要：从贝叶斯角度出发对部分线性单指标复合分位回归模型展开研究,并将其用于非寿险精算领域中的累积索赔金额数据建模.文中在建模过程中,考虑到数据中常见的解释变量缺失,在复合分位回归的目标函数中进行加权,然后基于复合非对称拉普拉斯分布(CALD)对模型中的参数采用贝叶斯方法进行估计.模型中单指标部分基于三次B-样条展开,为了减少模型中的待估参数,B-样条的系数给定狄利克雷过程先验.文章的主要贡献包括:一、首次从贝叶斯角度出发对部分线性单指标复合分位回归模型进行研究;二、考虑到解释变量的缺失,对复合分位回归的目标函数进行加权,其权重由logistic回归结果确定;三、将文章的模型运用于非寿险精算领域中的累积索赔金额预测中,从模型结果可看出,文章中所提方法比现有方法更优.From the Bayesian point of view,this paper studies partial linear singleindex composite quantile regression model,which is used in the modeling of cumulative claim amount data in the field of non-life insurance actuarial field.In the modeling process,taking into account the common missing explanatory variables in the data,weighting is carried out in the objective function of the composite quantile regression,and then based on the composite asymmetric Laplacian distribution(CALD),the parameters are estimated.In the single-index part,the cubic B-splines is used to fit the nonlinear effect.In order to reduce the parameters to be estimated in the model,the Dirichlet Process Prior is used.The main contributions of this paper include:1)It is the first time to study partial linear single-index composite quantile regression models from a Bayesian perspective;2)Taking into account the missing of explanatory variables,the weighted composite quantile regression is studied and its weight determined by the logistic regression result;3)Applying the model of the paper to the cumulative claim amount prediction in the field of non-life insurance actuarial field,from the model results,it can be seen that the method proposed in this paper is better than the existing methods.

关 键 词：复合分位回归 贝叶斯 单指标 累积索赔金额 

分 类 号：O212.1[理学—概率论与数理统计]