缺失数据下的逆概率多重加权分位回归估计及其应用  

Inverse Probability Multiple Weighted Quantile Regression Estimation and its Application with Missing Data

作　　者：邰凌楠 王春雨[1] 田茂再[2] Tai Lingnan;Wang Chunyu;Tian Maozai

机构地区：[1]中国人民大学统计学院 [2]教育部人文社会科学重点研究基地中国人民大学应用统计科学研究中心

出　　处：《统计研究》2018年第9期115-128,共14页Statistical Research

基　　金：中国人民大学科学研究基金(中央高校基本科研业务费专项资金资助)项目“大数据分析的稳健统计理论与应用研究”(18XNL012)的资助

摘　　要：数据缺失问题普遍存在于应用研究中。在随机缺失机制假定下,本文从模型推断角度出发,针对线性缺失分位回归模型,提出一种新的有效估计方法——逆概率多重加权(IPMW)估计。该方法是在逆概率加权(IPW)估计的基础上,结合倾向得分匹配及模型平均思想,经过多次估计,加权确定最终参数估计结果。该方法适用于响应变量是独立同分布或独立非同分布的情形,并适用于绝大多数数据缺失场景。经过理论推导及模拟研究发现,IPMW估计量在继承IPW估计量的优势上具有更稳健的性质。最后,将该方法应用于含有缺失数据的微观调查数据中,研究了经济较发达的准一线城市中等收入群体消费水平的影响因素,对比两种估计方法的估计结果,发现逆概率多重加权估计量的标准偏差更小,估计结果更稳健。In the practical research,there is always an issue of missing data. This paper proposes a new effective estimation,inverse probability multiple weighted（ IPMW） estimator,which is under MAR to deal with the problem of missing data in the linear quantile regression（ QR） from the perspective of model inference.This method is based on the traditional inverse probability weighted（ IPW） estimator,combined with the propensity score matching and the idea of model average. This method applies to situations where the response variable is independent and identically distributed（ IID） or independent and identically distributed（ INID） and also applicable to most missing scenarios. Based on the theoretical and simulation study,it is found that IPMW estimator is more robust than the traditional IPW estimator. Finally,by applying the IPMW to missing survey data,this paper analyzes the influence factors of consumption in middle income group and the different features of consumption among middle income group,and finds the SD of IPMW estimator is smaller than IPW estimator,and the estimation results are more robust.

关 键 词：线性分位回归 倾向得分 逆概率多重加权 随机缺失机制 模型平均 

分 类 号：O212[理学—概率论与数理统计]