完全辅助信息下非参数模型校准估计方法研究  

The Study on Calibration Estimation Method of Non-parametric Model with Complete Auxiliary Information

作　　者：贺建风 陈茜儒 陈飞 HE Jian-feng;CHEN Qian-ru;CHEN Fei(School of Economics and Finance,South China University of Technology,Guangzhou 510006,China;Management Committee of Shuangfeng Economic Development Zone,Hefei 231100,China)

机构地区：[1]华南理工大学经济与金融学院,广东广州510006 [2]安徽长丰双凤经济开发区管理委员会,安徽合肥231100

出　　处：《统计与信息论坛》2020年第11期23-32,共10页Journal of Statistics and Information

基　　金：国家社会科学基金项目“大数据背景下随机抽样技术及模型辅助估计方法研究”(19BTJ022);全国统计科学研究重大项目“大数据背景下抽样调查方法的改进及其应用研究”(2020LD02)。

摘　　要：大数据时代背景下,在现代化抽样调查实践中,一方面采集到各总体单位的完全辅助信息可以实现,能够利用完全辅助信息进行抽样估计,另一方面研究变量与辅助变量之间常呈现出非线性关系。在此情况下,如果仍然采用基于部分辅助信息的线性假定下的传统校准估计方法进行抽样估计,将存在信息浪费且估计方法不适用等缺陷。为解决以上两个问题,构建了完全辅助信息下的非参数模型校准估计方法体系,首先,将已有的校准估计方法归纳为基于部分辅助信息的传统校准估计和基于完全辅助信息的模型校准估计,然后,给出完全辅助信息下非参数模型校准估计量构建的基本思路,并提出基于局部多项式和惩罚样条两种具体类型的非参数模型校准估计量。研究发现,构建的非参数估计量具有设计无偏性、渐近正态性和一致性等优良的统计性质。进一步的模拟研究表明,非参数模型校准估计方法具有很强的适应性,且估计效率明显高于HT估计量和传统的校准估计量。In the era of big data big data,in the practice of modern sampling survey,it is possible to collect the complete auxiliary information of each population unit,and can use the complete auxiliary information to estimate the sampling.On the other hand,there is a nonlinear relationship between research variables and auxiliary variables.In the case,if the traditional calibration estimation methods based on linear assumption based on partial auxiliary information is still used for sampling estimation,there will be some defects such as information waste and the estimation method is not applicable.In order to solve the above problems,a system of non-parametric model calibration estimation method with complete auxiliary information is constructed,the existing calibration estimation methods are classified into traditional calibration estimation based on partial auxiliary information and model calibration estimation based on full auxiliary information,the basic idea of constructing non-parametric model calibration estimator with complete auxiliary information is given,a non-parametric model calibration estimator based on local polynomial and penalty spline is proposed.It is proved that the constructed non-parametric estimators have excellent statistical properties such as design unbiasedness,asymptotic normality and consistency.Further simulation results show that the non-parametric model calibration estimation method has strong adaptability,and the estimation efficiency is significantly higher than HT estimator and traditional calibration estimator.

关 键 词：完全辅助信息 非参数 模型校准估计 抽样调查 

分 类 号：C811[社会学—统计学]