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针对市县域样本量不足情况下的有效推断估计问题，本文在充分考虑复杂多阶段抽样机制的基础上，构建一套适用于我国住户调查市县域推断的区域层次模型小域估计方法。该模型由链接模型和抽样模型两部分构成。首先，本文通过链接模型融合来源准确的域层次辅助信息。其次，在抽样模型中引入Hájek估计量，充分利用住户调查复杂抽样设计信息，以处理市县域样本量的随机性问题；基于GVF函数的平滑估计，降低抽样误差的方差参数估计的不稳定性及波动性。进而，在符合住户调查市县域推断情况的区域层次模型下，推导EBLUP-Hájek小域估计量及其统计性质。最后，通过模拟和实证应用验证该市县域推断方法的有效性，为其他大规模抽样调查下的地方性推断估计工作提供有效参考。
Abstract：To address the problem of effective inference and estimation for city and county level domains with insufficient sample sizes, this paper proposes a small area estimation method based on an area-level model for city and county level inference in China's household survey, while fully accounting for the complex multistage sampling mechanism. The proposed model consists of a linking model and a sampling model. Specifically, the linking model incorporates area-level auxiliary information from reliable sources, whereas the sampling model introduces a Hájek estimator to make full use of the complex sampling design information in the household survey and to account for the randomness of sample sizes for cities and counties. In addition, a smoothed estimation based on the GVF function is adopted to reduce the instability of variance parameter estimation for sampling errors. Under the resulting area-level model for city and county level inference in the household survey, the EBLUP-Hájek small area estimator and its statistical properties are derived. Finally, simulation studies and an empirical application are conducted to examine the effectiveness of the proposed method, which provides a useful reference for local inference and estimation in other large-scale sample surveys.
[1]陈光慧,刘建平.构建新时代现化统计调查体系的问题研究[J].统计研究, 2018, 35(6):11–17.
[2]巩红禹,金勇进.住户调查中代表性样本的一种探索获取方法——平衡抽样设计[J].统计研究, 2015, 32(9):84–90.
[3]国家统计局农村司课题组,赵建华.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, 29(9):73–79.
[4]贺建风,付永超,熊健.基于分层贝叶斯广义线性模型的小域估计方法研究[J].数理统计与管理, 2019, 38(2):247–260.
[5]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(14):55–58.
[6]李采霞,于力超.考虑时空效应的小域估计模型的理论发展与应用研究[J].数理统计与管理, 2026, 45(1):49–66.
[7]李莉莉.基于Brewer抽样的不放回样本追加策略下域的估计[J].数理统计与管理, 2017, 36(4):651–660.
[8]刘建平.辅助信息在抽样调查中的应用模型与方法[M].北京:中国统计出版社, 2008:270–286.
[9]栾文英.永久随机数法抽样技术的有关问题研究[M].北京:经济科学出版社, 2020:71–97.
[10]刘晓宇,蒋妍.基于抽样权数调整的非参数分层贝叶斯模型小域估计方法研究[J].系统科学与数学, 2023, 43(12):3312–3323.
[11]吕萍.抽样调查中域类型的研究[J].调研世界, 2018(2):49–54.
[12]孟杰,邹文慧,杨贵军,等.合成估计方法在季度工资总额小域估计中的应用研究[J/OL].数理统计与管理, 1–13.
[13]孙婕,金勇进,戴明锋.我国政府统计中多层次推断问题讨论[J].统计研究, 2013, 30(9):3–9.
[14]谭馨,陈光慧.不放回样本追加下基于永久随机数抽样技术的多层次推断方法及应用研究[J].统计研究, 2024, 41(8):139–149.
[15]万舒晨.规模以下工业抽样设计研究[J].统计研究, 2021, 38(6):116–127.
[16]Battese G E, Harter R M, Fuller W A. An Error-Components Model for Prediction of County Crop Areas Using Survey and Satellite Data[J].Journal of the American Statistical Association, 1988, 83(401):28–36.
[17]Burgard J P, Esteban M D, Morales D, et al. A Fay-Herriot Model When Auxiliary Variables Are Measured with Error[J]. Test, 2020, 29(1):166–195.
[18]Drew D, Singh M P, Choudhry G H. Evaluation of Small Area Estimation Techniques for the Canadian Labour Force Survey[J]. Survey Methodology, 1982, 8(1):17–47.
[19]Fay R E, Herriot R A. Estimates of Income for Small Places:An Application of James-Stein Procedures to Census Data[J]. Journal of the American Statistical Association, 1979, 74(2):269–277.
[20]Ghosh M, Rao J N K. Small Area Estimation:An Appraisal[J]. Statistical Science, 1994, 9(1):55–76.
[21]Gonzalez M E, Hoza C. Small-Area Estimation with Application to Unemployment and Housing Estimates[J]. Journal of the American Statistical Association, 1978, 73(361):7–15.
[22]Liu L, Hudgens M G, Becker-Dreps S. On Inverse Probability-Weighted Estimators in the Presence of Interference[J]. Biometrika, 2016, 103(4):829–842.
[23]Hidiroglou M A, Beaumont J F, Yung W. Development of a Small Area Estimation System at Statistics Canada[J]. Survey Methodology, 2019,45(1):101–126.
[24]Iseh M J, Enang E I. A Calibrated Synthetic Estimator for Small Area Estimation[J]. Statistics in Transition New Series, 2021, 22(3):15–30.
[25]Purcell N J, Kish L. A Biometrics Invited Paper. Estimation for Small Domains[J]. Biometrics, 1979, 35(2):365–384.
[26]Rao J N K, Molina I. Small Area Estimation[M]. John Wiley&Sons, 2015:123–169.
[27]You Y. Small Area Estimation Using Fay-Herriot Area Level Model with Sampling Variance Smoothing and Modeling[J]. Survey Methodology,2021, 47(2):361–371.
(1)因篇幅所限，WLS法求解最优线性无偏小域估计量过程以附录1展示，见《统计研究》网站所列附件。下同。
(2)因篇幅所限，GVF法平滑处理抽样误差de的方差参数估计值■过程以附录2展示。
(3)因篇幅所限，矩阵形式下EBLUP估计向量推导各市县域EBLUP估计量过程以附录3展示。
(1)因篇幅所限，方差式■的推导过程以附录4展示。
(1)因篇幅所限，估计效果指标ARB、CV、MV的具体公式以附录5展示，各市域关于各类估计量的估计值、评价指标值以附表1~2展示。
基本信息:
DOI：10.19343/j.cnki.11-1302/c.2026.06.010
中图分类号:F299.23;C81
引用信息:
[1]陈光慧,董媚.基于区域层次模型小域估计的住户调查市县域推断方法及应用研究[J].统计研究,2026,43(06):131-146.DOI:10.19343/j.cnki.11-1302/c.2026.06.010.
基金信息:
全国统计科学研究重大项目“构建与高水平社会主义市场经济体制相适应的统计调查体系研究”（2024LD001）; 全国统计科学研究重点项目“基于小域估计方法的住户调查市县域数据评估研究——以广东为例”（2022LZ40）
2024-08-20
2024
2026-04-15
2026-04-27
2026
2
2026-06-25
2026-06-25