基于交叉子总体的抽样设计及其估计方法研究  

The Sampling Design and Estimation Method Based on Overlapping Sub-population

作　　者：陈光慧[1] 吴钰冰 Chen Guanghui;Wu Yubing

机构地区：[1]暨南大学经济学院统计学系 [2]暨南大学经济学院

出　　处：《统计研究》2020年第8期77-90,共14页Statistical Research

基　　金：国家社会科学基金一般项目“建立中国政府现代统计调查体系的问题研究”(18BTJ005)。

摘　　要：在抽样调查中,随着当前经济社会的变化和发展,调查对象及其目标总体的范围和结构日益复杂。基于单个调查总体构建单一的抽样框进行随机抽样的传统调查方式往往存在较大问题,如单个调查总体的抽样框覆盖不全,单一抽样框的更新和维护成本又过高。本文认为,基于交叉子总体开展抽样设计及其估计是解决上述难题的有效方法。针对交叉子总体的抽样设计,本文在现行Hartley估计方法的基础上,引入了辅助变量信息和超总体模型,提出了一种基于广义回归估计方法的新型Hartley-GREG估计量,并进一步研究了其在二阶抽样下的具体估计量形式。另外,考虑到辅助变量信息不完备的情形,分别提出了基于双边和单边辅助信息的Hartley-GREG-Bs和Hartley-GREG-Ss估计量。本文还通过理论和数值模拟对几类新型的估计量与传统的Hartley、F-B估计量进行分析比较。数值模拟结果表明:在一般情形下,本文提出的几类新型估计量的估计精度比传统的Hartley、F-B估计量更高。最后,本文以我国规模以下工业企业抽样调查为例,具体给出了基于规下工业企业交叉子总体的抽样方案和新型的广义回归估计程序,从而更好地验证了本文研究的这一套理论方法的推广应用价值。With the change and development of today’s economy and society,the objects in sampling survey and the scope and structure of the population are getting more complicated.The traditional random sampling with a single sample frame may cause many problems,such as incomplete coverage and high cost of maintaining and updating of a single sampling frame.This paper holds that the sampling design and estimation based on overlapping sub-population is an effective method to solve these problems.With the generalized regression estimation method,we propose a new estimator named Hartley-GREG based on Hartley estimation method and introduce auxiliary variable information and super-population model.Also,its estimator form under the second-order sampling is studied.Considering the incomplete auxiliary variables,estimators based on bothside and single-side auxiliary information are proposed,namely Hartley-GREG-Bs and Hartley-GREG-Ss respectively.The new and traditional estimators such as Hartley and F-B are compared from both theory and numerical simulation,which shows that the accuracy of the new estimators proposed in this paper is higher than that of traditional estimators in most situations.At last,this paper takes a sampling survey of China’s industries under the designated scale as an example to show the promotion and application value of the new method,and gives the specific sampling scheme as well as the new generalized regression estimation program based on the overlapping sub-population of industrial enterprises under the designated scale.

关 键 词：交叉子总体 抽样设计 超总体模型 Hartley估计量 广义回归估 

分 类 号：C811[社会学—统计学]