线性测量误差模型中的一类两参数估计  

A Two-Parameter Estimator in Linear Measurement Error Model

作　　者：左卫兵 李慧慧 ZUO Wei-bing;LI Hui-hui(School of Mathematics and Statistics,North China University of Water Resources and Electric Power,Zhengzhou 450046,China)

机构地区：[1]华北水利水电大学数学与统计学院

出　　处：《兰州文理学院学报（自然科学版）》2020年第1期1-7,共7页Journal of Lanzhou University of Arts and Science(Natural Sciences)

基　　金：河南省基础与前沿技术研究项目(142300410401)

摘　　要：针对线性测量误差模型中解释变量存在复共线性问题,提出线性测量误差模型中的一类两参数估计,该估计是最小二乘估计、Liu估计和岭估计的推广,并给出该估计渐近正态性.在均方误差矩阵意义下,得到该估计优于最小二乘估计、Liu估计以及岭估计的充要条件.最后,通过蒙特卡洛模拟方法验证其优良性.The parameter estimation problem is considered when the explanatory variables multicollinearity exists in linear measurement error model and a two-parameter estimator(TPE)is proposed in linear measurement error model.The estimator is a generalization of the least squares estimator(LSE),the Liu estimator(LE)and the ridge estimator(RE)and the property of the asymptotic normal distribution is obtained.In the sense of the mean square error matrix,the necessary and sufficient conditions for the superiority of the TPE over the LSE,the LE and the RE are derived.Finally,its superiority is verified by Monte Carlo simulation.

关 键 词：线性测量误差模型 复共线性 两参数估计 均方误差矩阵 蒙特卡洛模拟 

分 类 号：O212.1[理学—概率论与数理统计]