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

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收藏 2011-01-07

【原文出处】数理统计与管理

【原刊地名】京

【原刊期号】20101

【原刊页号】88～101

【分类号】F104

【分类名】统计与精算

【复印期号】201003

【英文标题】Empirical Likelihood Confidence Intervals for Quantile Differences in Response Variables of Two Linear Regression Models under Random Imputation

【标题注释】【基金项目】国家自然科学基金(10971038)；广西科学基金(0728092)；教育部留学回国人员科研启动资金([2004]527)。

【作者】罗志军/王历容

【作者简介】罗志军，湖南人文科技学院数学系；

王历容，湖南娄底技师学院（湖南　娄底　417000），广西师范大学数学科学学院（广西　桂林　541004）。

【内容提要】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，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。

【摘要题】理论与方法

【英文摘要】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 . 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.

【关键词】线性模型/分位数/缺失数据/随机回归插补/经验似然/置信区间

linear model/quantile/missing data/random regression imputation/empirical likelihood/confidence intervals

【正文】

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