泊松计数回归模型以及在汽车保险理赔欺诈行为中的应用  

The Poisson Count Regression Model with Its Application to the Fraud in the Vehicle Insurance

作　　者：吴琴[1] 刘寅[2] 田国梁 WU Qin;LIU Yin;TIAN Guo-liang(School of Mathematical Science,South China Normal University,Guangzhou 510006,China;School of Statistics and Mathematics,Zhongnan University of Economics and Law,Wuhan 510640,China;Department of Mathematics,Southern University of Science and Technology,Shenzhen 518055,China)

机构地区：[1]华南师范大学数学科学学院,广东广州510006 [2]中南财经政法大学统计与数学学院,湖北武汉510640 [3]南方科技大学数学系,广东深圳518055

出　　处：《数理统计与管理》2020年第4期611-616,共6页Journal of Applied Statistics and Management

基　　金：国家自然科学基金青年项目(11401226,11601524,11771199);广东省自然科学基金博士启动基金(2017A030310264)。

摘　　要：泊松计数方法作为估计敏感性特征的比例的方法,克服了项目计数方法泄露被调查隐私的缺陷。但是很多实际问题中,我们关心的不仅是敏感性特征的比例,更加感兴趣的是敏感性特征比例与协变量之间的关系。本文将提出基于泊松计数方法的回归模型,研究敏感性特征比例与协变量之间的相关性。我们给出了如何用EM算法和QLB算法求回归系数的极大似然估计。并且,我们搜集了399位被调查者关于美国车险理赔中的欺诈的行为以及关于驾驶习惯的协变量,并用我们的泊松计数回归模型进行研究,得到有用的信息。The Poisson Count Technique is proposed to estimate the proportion with sensitive characteristic,and it overcomes the leak of privacy in the Item Count Technique.However,we are more interested in the relationship between the proportion and the covariates rather than the proportion only.In this paper,we will introduce the Poisson Count Regression Model to investigate the correlation between the sensitive proportion and the covariates.We present how to use the EM algorithm and QLB algorithm to calculate the MLEs of the coefficients in the regression model.Moreover,we collected the data of 399 interviewees in America to investigate the fraud in the vehicle insurance and their related covariates.Our proposed Poisson Count Regression Model is employed to analyze the data to obtain useful information.

关 键 词：车险欺作 泊松计数方法 回归模型 EM算法 QLB算法 

分 类 号：O212[理学—概率论与数理统计]