基于结构风险最小化原则的线性EIV模型参数岭估计方法  

Structural Risk Minimization Principle-Based Linear EIV Model with Parameter Ridge Estimation Method

作　　者：赵明清 席甜甜 ZHAO Ming-qing;XI Tian-tian(School of Mathematics and Systems Science,Shandong University of Science and Technology,Qingdao 266590,China)

机构地区：[1]山东科技大学数学与系统科学学院,山东青岛266590

出　　处：《数理统计与管理》2020年第5期874-883,共10页Journal of Applied Statistics and Management

基　　金：山东科技大学研究生导师指导能力提升计划立项项目(KDYC17018);山东科技大学专业学位研究生教学案例库建设项目(SKDYAL17010).

摘　　要：加权整体最小二乘(WTLS)法是一种可同时顾及被解释变量和解释变量随机误差的估计方法,能够达到较高的预测精度.但是,该方法只考虑了模型的拟合优度,而忽略了复杂度,从而降低了其泛化能力.本文基于结构风险最小化原则,提出了线性EIV模型参数岭估计(PRE)方法,利用Lagrange乘数法导出了参数最优估计所满足的条件方程,并在此基础上给出了其数值解的迭代算法.为说明PRE方法的有效性,本文通过蒙特卡洛方法进行了数据模拟,进一步利用PRE方法对1995 2016年我国财险保费收入影响因素进行了实证研究,并与最小二乘(LS)、岭估计(RE)和加权整体最小二乘(WTLS)三种方法对比,研究结果表明:本文提出的PRE方法能明显提高预测精度,具有更强的泛化能力等优点.本文的最后还提出了PRE的统计性质等几个需要进一步研究的问题.Weighted Total Least Squares(WTLS)is an estimation method that can take into account the random errors of the interpreted and explanatory variables at the same time,which can achieve high prediction accuracy.However,this method only considers goodness of fit,but ignores the complexity of the model,which reducing its generalization ability.In this paper,considering the principle of structural risk minimization,the linear EIV model with parameter ridge estimation(PRE)method is proposed.The Lagrange multiplier method is used to derive the conditional equation that satisfies parameter optimal estimation,an iterative algorithm for its numerical solution is given too.In order to better illustrate the effectiveness of the PRE method,this paper carried out data simulation by Monte Carlo method.Then we conduct the empirical study on the influencing factors of China’s property insurance premium income during 1995-2016 using the PRE method,and compared with least squares(LS),traditional the ridge estimation(RE)and weighted total least squares(WTLS)method.The research results show that the PRE method proposed in this paper can achieve higher precision,generation et.al.At the end of the paper,several statistical issues such as the statistical nature of PRE are proposed.

关 键 词：EIV模型 参数估计 结构风险最小化原则 财险保费收入 

分 类 号：O212[理学—概率论与数理统计]