随机插补下两线性模型中响应变量分位数差异的经验似然置信区间

Empirical Likelihood Confidence Intervals for Quantile Differences of Response Variables in Two Linear Regression Models under Random Imputation

设两个样本数据不完全的线性模型，其中协变量的观测值不缺失，响应变量的观测值随机缺失。采用随机回归插补法对响应变量的缺失值进行补足，得到两个线性回归模型的“完全”样本数据，在一定条件下得到两响应变量分位数差异的对数经验似然比统计量的极限分布为加权X1^2，并利用此结果构造分位数差异的经验似然置信区间。模拟结果表明在随机插补下得到的置信区间具有较高的覆盖精度．

Consider two linear regression models with missing data. Suppose that the covariates are not missing, but response variables are missing at random. Random regression imputation method is used to impute the missing data of response variables and obtain ＇complete＇ data for two linear regression models. Under some conditions, it is proved that the asymptotic distributions for the empirical log-likelihood ratios of quantile differences of response variables are scaled X1^2. Empirical likelihood confidence intervals for quantile difference of response variables are then constructed based on these results. Simulations show that fractional imputation can improve the coverage accuracy of confidence intervals.