基于分层贝叶斯广义线性模型的小域估计方法研究

The Study of Small Area Estimation Method Based on Hierarchical Bayesian Generalized Linear Model

当前,构建恰当的小域估计方法是解决我国政府抽样调查中多层次推断问题的关键所在。由于小域的小样本特性,基于频率统计学的小域估计方法推断效果并不理想,而传统基于贝叶斯统计视角的小域估计方法在非连续型变量估计时适应性不强。本文在系统介绍传统贝叶斯小域估计方法的基站上,为了解决离散变量的估计推断问题,将广义线性模型引入到分层贝叶斯方法中,构建了基本的理论机制和分类数据的估计模型。基于此模型,运用全国流动人口动态监测调查2014年广东省内的样本数据进行实例测算,估计出广东省各地级市的流动人口学历分布情况,并将分层贝叶斯广义线性模型的估计结果与传统估计方法进行了对比分析。结果显示,分层贝叶斯广义线性模型在样本量充足的情况下能够准确地估计出目标小域的总体参数,在样本量不足的小域中依然能够给出稳健的估计结果。文章所构建的估计模型不仅可以充分利用先验信息和辅助信息,还适用于对复杂数据进行估计推断,能够为我国政府抽样调查的小域估计实践提供有价值的理论参考。

At present,the key to solve the problem of multi-level inference in Chinese government sample survey is to construct the appropriate small domain estimation method.Because of the small sample characteristics,the effect of small area estimation based on frequency statistics is not satisfactory.However,the traditional Bayesian small area estimation methods are not adaptable to the discontinuous variable estimation.This paper systematically introduces the traditional Bayesian small area estimation methods,and pulls generalized linear model into the hierarchical Bayesian method for solving the problem of discrete variables estimation inference.And then constructs the basic theoretical mechanism and the estimation model of classified data.Base on this model,the Guangdong Province’ssamples of China floating population dynamic monitoring survey in 2014 are used to estimate the educational distribution of floating population in each prefecture-level city of Guangdong Province,and estimation results of hierarchical Bayesian generalized linear model are compared with those of traditional estimation methods.The results show that the hierarchical Bayesian generalized linear model can accurately estimate the total parameters of the target domain when the sample size is sufficient.The new estimation model not only makes full use of prior information and auxiliary information,but also can be used to estimate complex data.It can provide valuable theoretical reference for the practice of small area estimation in our government sample survey.