缺失数据均值推断的经验似然方法  

Empirical Likelihood Method for Mean Inference with Missing Data

作　　者：郁文[1] 郑明[1] 

机构地区：[1]复旦大学管理学院统计学系,上海200433

出　　处：《数学年刊（A辑）》2010年第1期71-80,共10页Chinese Annals of Mathematics

基　　金：国家自然科学基金(No.10971033);上海市重点学科建设基金(No.B210)资助的项目

摘　　要：研究了缺失数据的均值推断问题.在随机缺失及半参数模型的假设下,设计了基于影响函数理论的经验似然推断方法,证明了所构造的对数经验似然比检验统计量具有非参数Wilks性质.此外,该经验似然方法可以利用辅助协变量中提供的附加信息来提高检验的功效.在近邻备择假设下,计算了检验统计量的功效,并且通过一些模拟考察了该方法在有限样本下的表现.The inference about the population mean of missing response data with auxiliary covariates is considered. Under the missing at random assumption and a semiparametric model, an empirical likelihood based inferential procedure is developed. An empirical likelihood ratio test statistic is constructed based on the influence function theory. A nonparametric version of Wilks＇ theorem is shown to hold for the empirical likelihood ratio. Moreover, the proposed method is capable of combining information from auxiliary covariates and providing a more powerful empirical likelihood ratio test. The asymptotic power function is calculated under contiguous alternatives. Some simulation studies are carried out to examine the finite sample performances of the proposed method.

关 键 词：随机缺失 插值 半参数模型 经验似然 辅助信息 

分 类 号：O212.1[理学—概率论与数理统计]