含方程误差的异方差重复测量误差模型参数估计  

Estimation of Heteroscedastic Replicated Measurement Error Model with Equation Error

作　　者：曹春正[1] 徐越[1] 王雅慧[1] 

机构地区：[1]南京信息工程大学数学与统计学院,江苏南京210044

出　　处：《数学的实践与认识》2015年第6期265-272,共8页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11301278);教育部人文社科基金(13YJC910001);江苏省自然科学基金(BK2012459)

摘　　要：对于含测量误差的重复测量数据,协变量与响应变量真值之间可能不存在完全匹配关系,即存在方程误差.且变量真值的测量误差方差可能与样本的某种特征有关,即存在异方差性.以此类数据为驱动,讨论了含方程误差的异方差重复测量误差模型的建模和估计问题,基于EM算法给出了模型参数的显式极大似然迭代估计.最后通过模拟计算和实例分析,讨论了模型和估计方法的有效性.For the data which contains measurement errors,true values of the covariates and the response may not completely match with each other due to the existence of equation error.Moreover,the variances of the measurement errors may have some relations with the characteristics of samples.Aiming at these data,we propose a heteroscedastic replicated measurement error model with equation error,and give an explicit iterative formulas of the maximum likelihood estimation via an EM type algorithm.The effectiveness of our model and estimation method are displayed through the simulation and a real data example.

关 键 词：测量误差 异方差 方程误差 极大似然估计 EM算法 

分 类 号：O212.1[理学—概率论与数理统计]