人口普查遗漏的组合式估计方法  

Combined Estimation Method for Census

作　　者：胡桂华[1,3] LOPEZ-CARR David 黄艳华 吴笛[1] HU Guihua;L PEZ-CARR David;HUANG Yanhua;WU Di(School of Mathematics and StatisticsChongqing Technology and Business University,Chongqing 400067,China;Research Institute for the Construction of the Chengdu-Chongqing Economic Circle,Chongqing Technology and Business University,Chongqing 400067,China;Department of Geography,University of California Santa Barbara,Santa Barbara 93106,America)

机构地区：[1]重庆工商大学数学与统计学院,重庆400067 [2]重庆工商大学成渝地区双城经济圈建设研究院,重庆400067 [3]加州大学圣芭芭拉分校地理系,加利福尼亚圣芭芭拉93106

出　　处：《统计与信息论坛》2024年第2期3-14,共12页Journal of Statistics and Information

基　　金：国家社会科学基金后期资助暨优秀博士论文项目“人口普查登记误差估计”(21FTBJ002)。

摘　　要：以人口普查标准时点上的人口总体(全国、全国以下各行政区)为研究对象,研究如何利用对总体登记的普查人口名单和覆盖调查人口名单构造的组合式遗漏估计量估计人口普查遗漏人口数。目前各国政府统计部门在人口普查遗漏估计中主要使用单重遗漏估计量,但该方法未包括同时遗漏于这两份调查人口名单的双重遗漏人口,低估了总体普查遗漏人口数。组合式遗漏估计量除了包括单重遗漏人口外,还包括了双重遗漏人口,避免了单重遗漏估计量的缺陷。采取抽样估计和数理模型相结合的方法研究单重遗漏估计量、双重遗漏估计量和组合式遗漏估计量,理论和数据分析结果表明:组合式遗漏估计量在抽样估计精度和遗漏人口数估计上优于单重遗漏估计量,尤其是在分析双重遗漏人口特征和改进未来人口普查登记工作等方面;在使用刀切法近似计算总体的组合式遗漏估计量的抽样方差时,不能忽视等概率人口层之间的协方差,否则可能低估或高估其抽样方差;单重遗漏估计量和组合式遗漏估计量属于有偏估计量,要使用均方误差比较其估计精度。本文创新之处在于,利用原始数据全面演示了单重遗漏估计量、双重遗漏估计量和组合式遗漏估计量及其抽样方差估计量等的详细计算过程,同时讨论了其统计性质,尤其是利用设置的数据模拟了有偏性,有助于中国人口普查遗漏估计方案的科学制定及估计精度的提高。The research object is the population(national and sub-national)at the standard point time of the census.It is examined how to estimate the number of census omissions using a combined-omission estimator constructed from the census population list,the coverage survey population list,and the matched population list of these two survey population lists.The research objective is to implement the proposed combined-omission estimator to replace the single-omission estimator currently recommended by the United Nations Statistics Division for countries.At present,government statistical departments in various countries mainly use the single-omission estimator in population census omission estimation.This omission estimator is established by the omitted population registered on the coverage survey population list but not on the census population list and its sampling weight.The single-omission estimator does not include the double omitted population that is omitted from both survey population lists,so it underestimates the overall population omitted in the census.The combined-omission estimator not only includes the single omitted population but also includes the double omitted population,thus avoiding the defects of the single-omission estimator.The combination method of sampling estimation and mathematical modeling is used to study the single-omission estimator,the double-omission estimator,the combined-omission estimator,and their biases,sampling variance and mean square error estimation.Results show that:The combined-omission estimator consists of a single-omission estimator and a double-omission estimator;The theoretical basis of the double-omission estimator is the capture-recapture model,which must be established in the equal probability population stratum,while the single-omission estimator does not need to be constructed in the equal probability population stratum;To facilitate the establishment of the combined-omission estimator,the single-omission estimator and the double-omission estimator can be established in

关 键 词：政府统计 人口普查质量评估 单重遗漏估计量 双重遗漏估计量 组合式遗漏估计量 不完整二维列联表 

分 类 号：O212[理学—概率论与数理统计]