From Conditional Quantile Regression to Marginal Quantile Estimation with Applications to Missing Data and Causal Inference
通过条件分位数回归提出两种新的边际分位数和均值估计方法，适用于结果变量随机缺失的情形，其中一种无需选择倾向得分，另一种对模型误设具有双重稳健性，并在因果推断中展示应用。
It is well known that information on the conditional distribution of an outcome variable given covariates can be used to obtain an enhanced estimate of the marginal outcome distribution. This can be done easily by integrating out the marginal covariate distribution from the conditional outcome distribution. However, to date, no analogy has been established between marginal quantile and conditional quantile regression. This article provides a link between them. We propose two novel marginal quantile and marginal mean estimation approaches through conditional quantile regression when some of the outcomes are missing at random. The first of these approaches is free from the need to choose a propensity score. The second is double robust to model misspecification: it is consistent if either the conditional quantile regression model is correctly specified or the missing mechanism of outcome is correctly specified. Consistency and asymptotic normality of the two estimators are established, and the second double robust estimator achieves the semiparametric efficiency bound. Extensive simulation studies are performed to demonstrate the utility of the proposed approaches. An application to causal inference is introduced. For illustration, we apply the proposed methods to a job training program dataset.