基于分层贝叶斯广义线性模型的小域估计方法研究
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摘要
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.
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.
引文
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[2] Ericson W A. A note on the posterior mean[J]. Journal of the Royal Statistical Society(Series B),1969, 31:332-334.
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[8] Pfeffermann D. New important developments in small area estimation[J]. Statistical Science,2013,28:40-68.
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[11]冯士雍.抽样调查应用与理论中的若干前沿问题[J].统计与信息论坛,2007,(1):5-13.
[12]吕萍.分位数回归模型在小域估计中的应用[J].统计教育,2009,(1):56-59+64
[13]国家统计局农村司课题组.小域估计方法在小品种农作物播种面积统计中的应用[J].统计研究,2012,(9):73-79.
[14]周巍,朱荣,张锦水.遥感辅助的农作物种植面积小域估计方法研究[J].统计研究,2015,(7):81-86.
[15]刘建华.复杂抽样小区域估计量的应用分析[D].中国疾病预防控制中心,2008.
[16]刘乐平,潘松权,任晓美.基于分层贝叶斯分析的残疾率小域估计方法[J].统计研究,2010,(3):83-88.
[17]潘松权.基于小域估计的我国居民膳食结构分析[D].天津财经大学,2011.
[18] Ghosh M, Rao J N K. Small area estimation:An appraisal[J]. Statistical Science, 1994, 9:55-76.
[19] Henderson C R. Estimation of genetic parameters(abstract)[J]. Ann. Math. Statist., 1950, 21:309-310.
[20] Morris C. Parametric empirical Bayes inference:Theory and applications(with discussions)[J]. J.Amer. Statist. Assoc, 1983, 78:47-65.
[21] Ghosh M. Hierarchical and empirical Bayes multivariate estimation[A]. In:Ghosh M, Pathak P K,(eds.). Current Issues in Statistical Inference:Essays in Honor of D Basu[C]. Hayward:IMS, 1992:151-177.
[22] Datta G S, Ghosh M. Bayesian prediction in linear models:Applications to small area estimation[J]. Ann. Statist., 1991, 19:1748-1770.
[23] McCullagh P, Nelder J A. Generalized Linear Models[M]. London:Chapman and Hall, 1989.
[24] Gelfand A E, andSmith A F M. Sampling-based approaches to calculating marginal densities[J].Journal of the American Statistical Association, 1990, 85:398-409.
[25] Gilks W R, Wild P. Adaptive rejection sampling for Gibbs sampling[J]. Applied Statistics, 1992, 41:337-348.
[26]邢春冰,贾淑艳,李实.教育回报率的地区差异及其对劳动力流动的影响[J].经济研究,2013,(11):114-126.
[2] Ericson W A. A note on the posterior mean[J]. Journal of the Royal Statistical Society(Series B),1969, 31:332-334.
[3] Stroud T W F. Hierarchical Bayes predictive means and variances with application to sample survey inference[J]. Communications in Statistics(Part A):Theory and Methods, 1991, 20:13-36.
[4] Stroud T W F. Bayesian inference from categorical survey data[J]. Canadian Journal of Statistics,1994, 22:33-45.
[5] Ghosh M, Natarajan K, Stroud T W F, Carlin B P. Generalized linear models for small-area estimation[J]. Journal of the American Statistical Association, 1998, 93:273-282.
[6] Ghosh M, Natarajan K, Waller L A, Kim D. Hierarchical Bayes GLMs for the analysis of spatial data:An application to disease mapping[J]. Journal of Statistical Planning and Inference, 1999, 75:305-318.
[7] Rao J N K, Small area estimation[M]. Lodon:Wiley, 2003.
[8] Pfeffermann D. New important developments in small area estimation[J]. Statistical Science,2013,28:40-68.
[9]金勇进,赵雪慧.对抽样调查解决多层次估计问题的探讨[J].统计研究,2003,(12):55-58.
[10]李莉莉.域估计的理论与方法[D].北京:中国科学院,2003.
[11]冯士雍.抽样调查应用与理论中的若干前沿问题[J].统计与信息论坛,2007,(1):5-13.
[12]吕萍.分位数回归模型在小域估计中的应用[J].统计教育,2009,(1):56-59+64
[13]国家统计局农村司课题组.小域估计方法在小品种农作物播种面积统计中的应用[J].统计研究,2012,(9):73-79.
[14]周巍,朱荣,张锦水.遥感辅助的农作物种植面积小域估计方法研究[J].统计研究,2015,(7):81-86.
[15]刘建华.复杂抽样小区域估计量的应用分析[D].中国疾病预防控制中心,2008.
[16]刘乐平,潘松权,任晓美.基于分层贝叶斯分析的残疾率小域估计方法[J].统计研究,2010,(3):83-88.
[17]潘松权.基于小域估计的我国居民膳食结构分析[D].天津财经大学,2011.
[18] Ghosh M, Rao J N K. Small area estimation:An appraisal[J]. Statistical Science, 1994, 9:55-76.
[19] Henderson C R. Estimation of genetic parameters(abstract)[J]. Ann. Math. Statist., 1950, 21:309-310.
[20] Morris C. Parametric empirical Bayes inference:Theory and applications(with discussions)[J]. J.Amer. Statist. Assoc, 1983, 78:47-65.
[21] Ghosh M. Hierarchical and empirical Bayes multivariate estimation[A]. In:Ghosh M, Pathak P K,(eds.). Current Issues in Statistical Inference:Essays in Honor of D Basu[C]. Hayward:IMS, 1992:151-177.
[22] Datta G S, Ghosh M. Bayesian prediction in linear models:Applications to small area estimation[J]. Ann. Statist., 1991, 19:1748-1770.
[23] McCullagh P, Nelder J A. Generalized Linear Models[M]. London:Chapman and Hall, 1989.
[24] Gelfand A E, andSmith A F M. Sampling-based approaches to calculating marginal densities[J].Journal of the American Statistical Association, 1990, 85:398-409.
[25] Gilks W R, Wild P. Adaptive rejection sampling for Gibbs sampling[J]. Applied Statistics, 1992, 41:337-348.
[26]邢春冰,贾淑艳,李实.教育回报率的地区差异及其对劳动力流动的影响[J].经济研究,2013,(11):114-126.