基于有偏误辅助变量的分层贝叶斯小域估计方法研究  

Hierarchical Bayesian Small Area Models with Biased Auxiliary Variables

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

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

出　　处：《统计与信息论坛》2024年第8期3-15,共13页Journal of Statistics and Information

基　　金：国家社会科学基金青年项目“大数据背景下的抽样调查理论及数据融合推断方法研究”(23CTJ027)。

摘　　要：抽样调查中的小域估计问题指的是,根据较少样本量进行一定精度下子总体估计的现实问题。与基于设计的方法不同,基于模型的方法不依赖大样本理论,能在估计过程中借助其他域的样本信息,更加适用于小域估计问题。然而,现实中测量误差无法完全避免,当模型协变量有偏误时,小域估计结果失效。对此,采用测量误差模型校正辅助变量误差,基于单元层次的分层贝叶斯模型进行小域估计,并在贝叶斯框架下估计辅助变量偏误机制。鉴于实际调查中为方便数据编码与统计、控制无回答误差,调查结果以分类型数据居多,本文重点讨论了更适用于小域估计问题的模型方法,针对分类型辅助变量存在测量误差的情形,给出了方法合理性的证明,同时通过模拟和实证对其估计效果进行验证与实践。本文模拟六种实践中常见的情形,除仅有分类型变量存在测量误差的情形之外,还考虑了存在测量误差的变量既有分类型又有连续型的情形等。数值模拟与实证结果一致表明,本文方法不仅能充分纳入与推断相关的不确定性因素,克服样本量受限的问题,还具有广泛的适用性,相较于传统方法,估计结果在提升准确度的同时更为稳健。The small area estimation problem in sampling survey refers to the practical problem of sub-population estimation under a certain accuracy with a small sample size.Different from the design-based method,the model-based method does not rely on large sample theory and can use sample information from other small areas in the estimation process,which is more suitable for small area estimation problems.However,in reality,measurement errors cannot be completely avoided.When the model covariates are measured with error,the small area estimation results will be invalid.In this regard,the measurement error model is adopted to correct the errors of auxiliary variables,which performs small area estimation based on the unit-level hierarchical Bayes model,and estimates the error mechanism of auxiliary variables under the Bayesian framework.In view of the fact that in actual surveys,in order to facilitate data coding and statistics and control non-response errors,the survey results are mostly categorical data.Therefore,focusing on a model method is more suitable for small area estimation problems.For the situation where categorical auxiliary variables have measurement errors,the rationality of the method is proved.At the same time,its estimation effect is verified and practiced through simulation and empirical studies.Six common situations are simulated in practice and in addition to the situation where only categorical variables have measurement errors,it also considers the situation where the variables with measurement errors including both categorical and continuous variables.Numerical simulations and empirical results consistently show that the method in this paper can not only fully incorporate uncertainty factors related to inference and overcome the problem of limited sample size,but also has broad applicability.Compared with traditional methods,the estimation results are more robust while improving accuracy.

关 键 词：小域估计 分层贝叶斯模型 测量误差模型 分类变量 GIBBS抽样 

分 类 号：C811[社会学—统计学]