基于多层次模型的小域估计方法研究——考虑抽样误差与测量误差的比率估计  

Small Area Estimation Method Based on Multi-level Model——Ratio Estimation Considering Sampling Error and Measure Error

作　　者：武雅萱 刘晓宇 Wu Yaxuan;Liu Xiaoyu(School of Statistics,Renmin University of China,Beijing 100872,China;School of Statistics,Capital University of Economics and Business,Beijing 100070,China)

机构地区：[1]中国人民大学统计学院,北京100872 [2]首都经济贸易大学统计学院,北京100070

出　　处：《统计与决策》2024年第7期52-56,共5页Statistics & Decision

基　　金：国家社会科学基金青年项目(23CTJ027)。

摘　　要：小域估计的核心在于如何对样本量极少甚至为0的域作出较为可靠的子总体特征估计。小域内样本量有限,即在估计时可利用的信息有限,最大程度挖掘样本信息并借助其他域样本推断本小域特征,是提高小域估计精度的关键。传统基于设计的推断效果受样本量制约,不适用于样本量有限的小域估计问题,此时,需要采用基于模型的方法进行估计。文章针对比率估计,基于多层次模型刻画有限总体和小域之间的层次结构,分别通过第一层模型和第二层模型刻画域间异质性和域间相关性,借助其他域的样本单元实现对指定小域的估计,并在此基础上考察抽样机制和测量误差的影响。针对所提出的模型,给出具体的参数估计与误差估计方法,通过模拟验证具体效果,并将其应用于实际数据集。The core of small area estimation is how to make a more reliable estimation of sub-population characteristics on the area with a very small sample size or even zero.The sample size in a small area is limited,that is,the information available for estimation is limited.Mining the sample information to the greatest extent and inferring the characteristics of this small area with the help of other area samples is the key to improving the accuracy of small area estimation.The traditional design-based inference effects are limited by sample size,which is not suitable for small area estimation with limited sample size.In this case,a model-based method is needed for estimation.For ratio estimation,this paper describes the hierarchical structure between the finite population and the small area based on the multi-level model.The level-one model and the level-two model are used to describe the heterogeneity and correlation between areas,and the sample units of other areas are used to estimate the specified small area.On this basis,the effects of the sampling mechanism and measurement error are examined.For the proposed model,the paper gives the specific parameter estimation and error estimation methods.The specific effects are verified through simulations and applied to real data sets.

关 键 词：小域估计 多层次模型 比率估计 

分 类 号：O212.1[理学—概率论与数理统计] C811[理学—数学]