缺失数据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 with Missing Data

总体差异的比较是医学,经济和教育领域中经常遇到的课题,本文讨论缺失数据情形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的构造。我们采用分数线性回归填补法对响应变量的缺失值进行补足,得到两线性回归模型的"完全"样本数据,在此基础上构造响应变量分位数差异的对数经验似然比统计量,在一定条件下证明了统计量的极限分布为加权χ12,并利用此结果构造分位数差异的经验似然置信区间。模拟结果表明在分数填补下得到的置信区间具有较高的覆盖精度。

The comparison of di？erences of populations is an important research topic in medical studies, economical and educational fields. This paper studies the construction of the quantile differences of response variables in two linear models with missing data. The fractional linear regression imputation method is used to impute the missing data of the response variables, and ‘complete’ data for two linear regression models are obtained. The empirical log-likelihood ratios of quantile differences of response variables are constructed based on the imputed data. Under some mild conditions, it is proved that the asymptotic distributions for the empirical log-likelihood ratios are scaled χ_1~2. The empirical likelihood confidence intervals for quantile differences of the response variables are then constructed based on this results. Simulations show that fractional imputation can improve the coverage accuracy of confidence intervals.