Applied Mathematics Seminar 8: From conditional quantile regression to marginal quantile estimation with applications to missing data and causal inference

This paper 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.