基于分层抽样的校准方法分别比率-乘积估计研究  

Research on the Calibration Approach Separate Ratio-Product Estimation Based on Stratified Sampling

作　　者：薛慧玲 陈光慧[2] XUE Hui-ling;CHEN Guang-hui(School of Statistics and Data Science,Jiangxi University of Finance and Economics,Nanchang 330013,China;School of Economics,Jinan University,Guangzhou 510632,China)

机构地区：[1]江西财经大学统计与数据科学学院,江西南昌330013 [2]暨南大学经济学院,广东广州510632

出　　处：《数理统计与管理》2023年第6期993-1009,共17页Journal of Applied Statistics and Management

基　　金：国家社会科学基金一般项目(18BTJ005);江西省教育厅一般项目(GJJ2200504);博士科研启动金(012273139)。

摘　　要：比率估计在抽样估计阶段利用辅助信息,提高了估计量的估计精度,是抽样调查中一类较为常用的估计方法,但现有的一些比率估计方法均具有各自的最优条件,这在一定程度上影响了它们在实际调查中的应用。为了解决比率估计的最优限制问题,本文引入了校准估计方法,并基于分层抽样研究了总体均值的校准方法分别比率-乘积估计量。在大样本情况下,本文推导了新估计量的估计偏差和均方误差,说明新估计量具有渐近无偏性,并在估计量均方误差最小时,得到了总体参数的渐近最优估计量和渐近最优估计量的方差。在模拟研究中,根据比率估计量的最优条件是否满足,本文生成了两种不同的总体,对比分析了新估计量和现有比率估计量的估计效果,结果表明在两种不同的情况下,新估计量的估计效果均优于现有估计量的估计效果。最后,本文利用一个实际例子,验证了新估计量的有效性和实用性。Ratio estimation uses auxiliary information in the sampling estimation stage to improve the estimation accuracy of the estimator.It is a commonly used estimation method in sample surveys.It is a kind of commonly used estimation method in the sampling survey,but some existing ratio estimation methods have their own optimal conditions,which affects their application in the actual survey to some extent.In order to address the problem of the optimal limitation of ratio estimation,this paper introduces the calibration estimation method,and studies the calibration approach separate ratio-product estimation of the population mean based on stratified sampling.In the case of large samples,this paper derives the estimation bias and mean square error of the new estimator,which shows that the new estimator is asymptotically unbiased,and when the mean square error of the estimator is the smallest,the asymptotic optimal estimator of population parameters and the variance of the asymptotic optimal estimator are obtained.In the simulation study,according to whether the optimal condition of the ratio estimator is met,this paper generates two different populations,and compares and analyzes the estimation effect of the new estimator and the existing ratio estimator.The results show that the estimation effect of the new estimator is better than that of the existing estimator under two different conditions.Finally,this article applies the estimator to a practical example to verify the validity and practicability of the new estimator.

关 键 词：分层抽样 辅助信息 校准估计 分别比率-乘积估计 最优估计 

分 类 号：C811[社会学—统计学] O212[理学—概率论与数理统计]