两样本密度比模型下的利用辅助信息的经验似然均值估计

在有限总体推断问题中,辅助总体信息是经常可获取的.经验似然方法已被证实是一种非常灵活和有用的工具来处理这类问题.在两样本密度比模型下,本文考虑了基准分布的总体均值的经验似然推断问题.对基于密度比模型的经验似然而言,对偶似然是一种便利的技术工具,尽管它与标准的经验似然具有相同的极值点和极值,但是它却不能方便地把此类辅助信息引入到似然函数里,因此会导致效率损失.相对而言,Qin和Lawless21]提出的标准的经验似然方法不会有此问题,且能方便地引入辅助信息.基于使用辅助信息的经验似然和对偶似然方法,我们构建了点估计和区间估计,并做了仔细的比较.模拟发现,尽管使用辅助信息的经验似然方法得到的点估计的效率提升很小,但是区间估计在一些情形下却有明显的差别.拿覆盖精度来说,在无偏或适当有偏的总体分布下,两种方法得到的区间估计是可比的,但当总体严重有偏时,前者的区间估计明显优于后者.

Empirical Likelihood Estimation for the Two-Sample Mean under Density Ratio Models Using Auxiliary Information

Auxiliary population information is often available in nite population inference problems, and the empirical likelihood (EL) approach has been demonstrated to be exible and useful for such problems. The present paper concerns EL when interest centers on inference for the mean of the baseline distribution under two-sample density ratio models. Although dual EL is a convenient technical tool since it has the same maximum point and maximum likelihood as DRM-based EL,it can not combine such auxiliary information into the likelihood conveniently and may have loss of efficiency. By contrast, the classical EL approach of Qin and Lawless 21] does not have this problem and incorporate seamlessly auxiliary information. Based on the EL using auxiliary information and the dual EL methods,we construct both point and interval estimations and make a careful comparison. Though the point estimation efficiency gain obtained by the former is not noticeable,we find that they may have different performances in interval estimation. In terms of coverage accuracy,the two intervals are comparable for not or moderate skewed populations,and the EL interval using auxiliary information can be much superior for severely skewed populations.