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本文对两个样本数据不完全的线性模型展开讨论, 其中线性模型协变量的观测值不缺失, 响应变量的观测值随机缺失(MAR). 我们采用逆概率加权填补方法对响应变量的缺失值进行补足, 得到两个线性回归模型``完全'样本数据, 在``完全'样本数据的基础上构造了响应变量分位数差异的对数经验似然比统计量. 与以往研究结果不同的是本文在一定条件下证明了该统计量的极限分布为标准, 降低了由于权系数估计带来的误差, 进一步构造出了精度更高的分位数差异的经验似然置信区间.

Empirical Likelihood Statistical Inference for Quantile Differences of Response Variables in Two Linear Regression Models after Inverse Probability Weighted Imputation

In this paper, we consider two linear models with
missing data, where the covariates are not missing, but response variables are missing
at random(MAR). The inverse probability weighted imputation is used to impute the missing
data of response variables, we can obtain the 'complete' data for two linear regression models.
Then we can construct the empirical log-likelihood ratios of quantile differences of response
variables. And the difference is that the asymptotic distributions for the empirical
log-likelihood ratios of quantile differences of response variables are standardcomparing with the results of previous studies. The empirical likelihood confidence
intervals for quantile difference of response variables is more accurate because the errors
caused right of the coefficient estimates is reduced.