人口普查的事后计数调查样本规模测算及分配  

Calculation and Allocation of Sample Size of Post-Enumeration Survey for Population Census

作　　者：胡桂华[1] 黄艳华[2] 吴笛 HU Guihua;HUANG Yanhua;WU Di(School of Mathematics and Statistics,Chongqing Technology and Business University,Chongqing 400067;Research Institute for the Construction of the Chengdu-Chongqing Economic Circle,Chongqing Technology and Business University,Chongqing 400067)

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

出　　处：《系统科学与数学》2024年第6期1821-1840,共20页Journal of Systems Science and Mathematical Sciences

基　　金：国家社科基金后期资助暨优秀博士论文一般项目(21FTJB002)资助课题。

摘　　要：文章旨在建立一套全新的事后计数调查样本规模测算和分配体系,以解决一些国家的政府统计部门未严格按照抽样理论测算和分配事后计数调查样本规模的问题.为实现目标,采用数理模型和参数估计方法计算2020年抽样方案(Q)的设计效应和2030年简单抽样方案(S)的样本规模,将两者相乘得到2030年抽样方案(Q)的样本规模.理论和实证结果表明:2020年抽样方案(Q)的设计效应为0.91,优于简单抽样方案(S);简单抽样方案(S)的单系统估计量无须在同质人口层建立,而抽样方案(Q)的组合式三系统估计量须在同质人口层构造;分层刀切法适合于近似计算组合式三系统估计量的抽样方差;比例分配法比最优分配法更适合于事后计数调查样本规模分配.创新之处在于,提出基于组合式三系统估计量和单系统估计量的抽样方差估计量的设计效应估计量,解释了用设计效应间接测算样本规模的数学逻辑.该成果有望作为国家统计局制定2030年事后计数调查样本规模测算与分配方案的重要参考,或被其采纳应用.This paper aims to establish a new system for calculating and allocating the sample size of post-enumeration surveys,in order to solve the problem that some governmental statistical departments in some countries do not strictly follow the sampling theory to calculate and allocate the sample size of post-enumeration surveys.To achieve the goal,mathematical models and parameter estimation methods are used to calculate the design effects of the 2020 sampling plan(Q)and the sample size of the 2030 simple sampling plan(S),and the two are multiplied to obtain the sample size of the 2030 sampling plan(Q).The theoretical and empirical results show that the design effect of the complex sampling plan(Q)in 2020 is 0.91,indicating that this sampling plan is better than that of the simple sampling plan(S);the single-system estimator of the simple sampling plan(S)need not be built in the homogeneous population stratum,while the combined three-system estimator of the sampling plan(Q)must be built in the homogeneous population stratum;the stratified jack-knife method is suitable for approximately calculating the sampling variance of the combined three-system estimator;the proportional distribution method is more suitable for the sample size allocation of the post-enumeration survey than the optimal allocation method.The innovation lies in proposing a design effect formula for sampling variance estimators based on combined three-system estimator and single-system estimator,and providing the mathematical logic for calculating sample size indirectly by design effect.This thesis is expected to serve as an important reference for the National Statistical Bureau to formulate the sample size calculation and allocation plan for the post-enumeration survey in 2030,or be adopted and applied.

关 键 词：政府统计 抽样调查 组合式三系统估计量 单系统估计量 抽样方差 

分 类 号：O212.2[理学—概率论与数理统计] C921[理学—数学]