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

摘要

The consistency and asymptotic normality of quasi-likelihood estimating equation as L(β) = ΣiZi(yi -μ(ZiTβ) ) =0 was considered when part of the covariates were incomplete in generalized linear 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 proposed 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.%研究了形如L(β)=Σ1Zi(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.