缺失数据下的逆概率多重加权分位回归估计及其应用

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及置信带，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。

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

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.