缺失数据下广义线性回归拟似然估计的相合性和渐近正态性  

Consistency and Asymptotic Normality of Quasi-likelihood Estimator in Generalized Linear Models with Missing Data

作　　者：赵晶晶[1] 张晓冉[1] 徐玉民[1] 

机构地区：[1]燕山大学理学院,河北秦皇岛066004

出　　处：《郑州大学学报（理学版）》2011年第3期43-47,共5页Journal of Zhengzhou University:Natural Science Edition

摘　　要：研究了形如L(β)=ΣiZi(yi-μ(ZiTβ))=0的拟似然方程在协变量数据有缺失时,方程未知参数估计的相合性和渐近正态性.假设存在协变量数据完整的一个有效样本,且是总样本的一个简单随机子样本,基于EM算法,提出了一种新的处理协变量中有不完整数据的拟似然方程的求解法,即通过有效数据线性预测补足协变量数据缺失部分,并且证明了当样本量n→∞,在满足一些正则条件下所得出的新拟似然方程有解,且该解具有相合性和渐近正态性.Abstract： The consistency and asymptotic normality of quasi-likelihood estimating equation as L（β）=∑iZi（yi—gμ（Zi^Tβ））=0 was considered when part of the covariates were incomplete in generalized models. It was assumed that there existed a validation sample in which the data was complete. And it was a simple random subsample from the whole sample. Based on the EM-solution, a new method was pro A posed to estimate the regression coefficients with incomplete covariables by linear predict the incomplete co-variable data. When it was sufficiently large, the estimate was consistency and asymptotic normality under some regularity conditions.

关 键 词：广义线性模型 拟似然估计 不完全协变量 相合性 渐近正态性 

分 类 号：O212.4[理学—概率论与数理统计]